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by Markus Knell and Alfred Stiglbauer
The ImpacT of RefeRence noRms on InflaTIon peRsIsTence When Wages aRe sTaggeRed
WoRk Ing papeR seR I e sno 1047 / apR I l 2009
WAGE DYNAMICSNETWORK
WORKING PAPER SER IESNO 1047 / APR I L 2009
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THE IMPACT OF REFERENCE NORMS
ON INFLATION PERSISTENCE
WHEN WAGES ARE STAGGERED 1
by Markus Knell 2 and Alfred Stiglbauer 3
and of various seminars for useful suggestions and comments. The views expressed in this paper do not necessarily reflect those of
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WAGE DYNAMICS
NETWORK
1 We thank Nils Gottfries, Steinar Holden, Andrew Levin, two anonymous referees and participants of the Wage Dynamics Network of the ECB
2 Corresponding author: Oesterreichische Nationalbank, Economic Studies Division, Otto-Wagner-Platz 3,
3 Oesterreichische Nationalbank, Economic Analysis Division, Otto-Wagner-Platz 3,
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This paper contains research conducted within the Wage Dynamics Network (WDN). The WDN is a research network consisting of economists from the European Central Bank (ECB) and the national central banks (NCBs) of the EU countries. The WDN aims at studying in depth the features and sources of wage and labour cost dynamics and their implications for monetary policy. The specific objectives of the network are: i) identifying the sources and features of wage and labour cost dynamics that are most relevant for monetary policy and ii) clarifying the relationship between wages, labour costs and prices both at the firm and macro-economic level. The WDN is chaired by Frank Smets (ECB). Giuseppe Bertola (Università di Torino) and Julian Messina (Universitat de Girona) act as external consultants and Ana Lamo (ECB) as Secretary. The refereeing process of this paper has been co-ordinated by a team composed of Gabriel Fagan (ECB, chairperson), Philip Vermeulen (ECB), Giuseppe Bertola, Julian Messina, Jan Babecký (CNB), Hervé Le Bihan (Banque de France) and Thomas Mathä (Banque centrale du Luxembourg). The paper is released in order to make the results of WDN research generally available, in preliminary form, to encourage comments and suggestions prior to final publication. The views expressed in the paper are the author’s own and do not necessarily reflect those of the ESCB.
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Working Paper Series No 1047April 2009
Abstract 4
Non-technical summary 5
1 Introduction 7
2 A model with wage staggering and reference norms 10
2.1 The set-up 10
2.2 The solution of the model 12
2.3 The role of different reference norms 14
2.4 Asymmetries in the importance of reference norms 16
3 Empirical part 18
3.1 Estimation equation 18
3.2 The Austrian system of collective wage bargaining 19
3.3 The data 20
3.4 Empirical strategy 23
3.5 Main results 24
3.6 Nested and non-nested tests on the importance of reference norms 26
3.7 An analysis of the individual heterogeneous coeffi cients 28
3.8 Further robustness tests 31
4 Conclusions 33
References 35
Appendices 39
Figures and tables 53
European Central Bank Working Paper Series 62
CONTENTS
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AbstractIn this paper we present an extension of the Taylor model with staggered wages in which wage-setting is also influenced by reference norms (i.e. by benchmark wages). We show that reference norms can considerably increase the persistence of inflation and the extent of real wage rigidity but that these effects depend on the definition of reference norms (e.g. how backward-looking they are) and on whether the importance of norms differs between sectors. Using data on collectively bargained wages in Austria from 1980 to 2006 we show that wage-setting is strongly influenced by reference norms, that the wages of other sectors seem to matter more than own past wages and that there is a clear indication for the existence of wage leadership (i.e. asymmetries in reference norms).
Keywords: Inflation Persistence, Real Wage Rigidity, Staggered Contracts, Wage Leadership
JEL Classification: E31, E32, E24, J51
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Non-Technical Summary
Standard models with nominal wage rigidities typically imply less inflation persistence
than can be found in empirical data (cf. Roberts, 1995; Fuhrer and Moore, 1995; Chari et
al., 2000). A common way to deal with this problem is to assume that a fraction of firms
use rule-of-thumb behavior or automatic indexation of their prices (cf. Christiano et al.,
2005; Smets and Wouters, 2007). These assumptions are, however, rather controversial
since the existing microeconomic evidence on price-setting is not in line with this kind of
behavior.
In this paper we analyze whether the process of wage-setting might be responsible for
the observed excessive persistence and the strong influence of backward-looking behavior.
The argument is based on the well-documented evidence from survey studies (cf. Bew-
ley, 1999; Agell and Bennmarker, 2007) that wage-setting is considerably influenced by
benchmark values that are typically related to past wage levels (e.g. to the workers’ own
past wages or to wages that have been previously set in other sectors of the economy).
This assumption of benchmark values (or reference norms) thus provides a plausible and
empirically validated way to make nominal variables more persistent.
The paper investigates this argument from both a theoretical and an empirical angle.
In the theoretical part we extend the classical, two period staggered-wage model by Taylor
(1980) to allow for reference norms. We show that the introduction of reference norms can
considerably increase inflation persistence in this standard framework. In a further step we
also demonstrate that the size of this impact depends on the precise type of the prevalent
reference norm and on whether the importance of reference norms differs between the
sectors of the economy. We discuss several different reference norms that correspond to
frequently made assumptions in the literature. As our benchmark specification we use
the assumption that the wage-setters are influenced by an “external norm”, i.e. they look
at the last wage level that has been set in the other sector. Different assumptions about
reference norms, however, have an effect on the exact amount of additional persistence.
A particularly important case in this context is the assumption of wage leadership where
the wage in one sector works as a reference norm for the other sector but not vice versa. A
structure of wage leadership is often said to be a good description of industrial relations
in a number of Scandinavian and continental European countries. We show that such
asymmetries in the importance of reference norms between sectors reduce the extent of
persistence considerably.
In the empirical part of the paper we use a unique dataset on collectively bargained
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wages in Austria from 1980 to 2006 to study the interplay between reference norms and
staggered wages. The dataset comprises around 100 individual wage-setting units covering
almost the complete national labor force. The data are well-suited to study these relations
since the process of Austrian wage-setting shows a clear structure of staggering and also
because it is often argued that the metal sector acts as a wage leader for the sectors
that follow. The data enable us to construct the reference norms that were discussed
in the theoretical part of the paper. The external reference norm is thus defined as the
average wage increase of all other units since the last wage settlement of the own unit
whereas the leadership norm is simply the wage increase in the metal sector. Moreover,
we also construct a “habit norm” (defined as the last increase of the own wage rate) and
a “standard of living” reference norm. Our main other explanatory variables for wages
are forecasts for real economic activity and inflation.
Our results indicate that reference norms are in fact an important factor for Austrian
wage settlements. By and large, the coefficient of the reference norm is slightly higher
than the coefficient of forecasted inflation. Of all reference norms considered, the wage
leadership norm performs best in the empirical analysis. This is based on parameter
restrictions derived from the theoretical model, on model specification tests as well as
on the results from a random coefficient model. In particular, we find that the wage-
leading sector reacts significantly stronger to the general macroeconomic outlook than
the following sectors.
Our findings have a number of consequences concerning inflation persistence and real
wage rigidity. First, reference norms are an important factor in wage-setting and they
need to be included in realistic and comprehensive dynamic macroeconomic models. Sec-
ond, in order to get a complete picture about the sources and consequences of nominal
rigidities it is important to study the microstructure of wage setting. Economies that
are characterized by differences in the importance of reference norms between sectors
will show less persistence than countries with a symmetric structure. Third, underlying
differences in reference norms could also be responsible for the observed cross-country
differences in inflation persistence and wage rigidities.
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1 Introduction
Numerous studies have documented that standard models with wage rigidities (like the
models by Taylor [1980] and Calvo [1983]) do produce considerably less endogenous per-
sistence in output and inflation than can be found in empirical data (cf. Roberts, 1995;
Fuhrer and Moore, 1995; Chari et al., 2000). The most common way to deal with this
problem is to assume that there exists some amount of additional intrinsic persistence in
prices. This is motivated, e.g., by the existence of “rule-of-thumb” price setters (cf. Galı
and Gertler, 1999) or by the assumption that all firms that do not reoptimize simply index
their prices to past inflation (cf. Christiano et al., 2005; Smets and Wouters, 2007). These
are useful short-cuts that help to bring the standard models with nominal rigidities closer
in line with the main properties of the observed data. Nevertheless, the assumptions of
automatic indexation and rule-of-thumb behavior are also controversial and they have
been criticized as being ad-hoc, implausible and at variance with the available evidence
on actual price-setting behavior of firms (cf. Mankiw and Reis, 2002; Rudd and Whelan,
2006).1
Given this controversial role of backward-indexation in price-setting it seems natural
to ask whether instead the process of wage-setting could be responsible for the observed
excessive persistence. In fact, there exists an extensive survey literature documenting that
wage-setting is affected by many more factors than can usually be found in standard labor
market models (cf. Campbell and Kamlani, 1997; Bewley, 1999; Agell and Bennmarker,
2007). In particular, it has been shown that actual wage-setting policies are considerably
influenced by benchmark values, e.g. by the workers’ own past wages or by the wages in
other sectors of the economy. Paying workers less than their benchmark value might cause
motivational problems with detrimental effects on morale and productivity. Interestingly,
these arguments from the labor market literature are only rarely incorporated into the
commonly used dynamic macroeconomic models. There exist some papers that take up
this line of thought but they differ in their focus and point of departure and they have also
not been clearly connected to the issue of backward indexation. Among these papers some
use models with relative wages (Buiter and Jewitt, 1981; Fuhrer and Moore, 1995; Ascari
and Garcia, 2004) while others are based on efficiency wages (Danthine and Kurmann,
2004) or wage norms (Hall, 2005; Gertler and Trigari, 2006). The common thread in this
1E.g. “Backward indexation of prices, an assumption which, as far as I know, is simply factually wrong,has been introduced to explain the dynamics of inflation. And, because, once they are introduced, theseassumptions can then be blamed on others, they have often become standard, passed on from model tomodel with little discussion” (Blanchard, 2008, 25).
8ECBWorking Paper Series No 1047April 2009
literature is that wage-setters are assumed to have (explicit or implicit) benchmark wages
or — as we will call them henceforth — reference norms that introduce an element of
backward-looking behavior and thereby contribute to real wage rigidities.
The paper contributes to the literature from both a theoretical and an empirical angle.
In the theoretical part we extend the classical, two period staggered-wage model by Taylor
(1980) to allow for reference norms. In the benchmark case the reference norm is specified
as an “external norm”, i.e. wage-setters are assumed to look at the last wage level that
has been set in the other sector. We show that the introduction of this reference norm
can considerably increase inflation persistence. In a further step we also demonstrate that
the size of this impact depends on the precise type of the prevalent reference norm and on
whether the importance of reference norms differs between the sectors of the economy. It
is crucial to take these issues into account since the empirical literature suggests that there
exist sizable differences along these lines both within and between countries. Campbell
and Kamlani (1997) and Bewley (1999), e.g., report that US workers mainly compare
their wage rate with their own past wages and with the wages of other workers within
the same firm (“internal reference norms”). Agell and Lundborg (2003) and Agell and
Bennmarker (2007), on the other hand, document a much larger role for external norms
in Sweden and considerable differences between Swedish and US survey data. In our
dynamic model the amount of persistence turns out to depend on the assumption about
the structure of reference norms, in particular on their degree of “backward-lookingness”
and on the importance of external (i.e. cross-sectional) comparisons.
As far as the possibility of asymmetric reference norms between sectors is concerned
it is important to note that it is frequently argued that a structure of “wage leadership”
is present in a number of Scandinavian and continental European countries.2 In such
a system a specific sector (mostly the metal sector) acts as a wage leader that sets its
wage levels more or less irrespective of what happens in the rest of the economy while the
other sectors will take this wage rate as their reference norm (cf. Smith, 1996; Lindquist
and Vilhelmsson, 2006; Traxler et al., 2008). Despite the empirical importance we know
of no paper that has studied wage leadership in the framework of standard dynamic
macroeconomic models. The set-up of our model allows us to tackle this issue. We
show that asymmetries in the importance of reference norms between sector reduce the
extent of persistence. This means that for two economies that are characterized by an
identical structure and an identical average importance of reference norms the economy
2In the literature one can find a number of synonymous expressions for this phenomenon like “payleadership”, “wage spillovers”, “pattern bargaining” or “key bargaining.”
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with asymmetric norms (e.g. wage leadership) will exhibit less persistence.
In the second part of the paper we then proceed to analyze whether the implications of
the model are more than just a theoretical possibility. An empirical test of the interplay
between reference norms and staggered wages requires a special kind of data that are not
easily available for many countries. In particular, one needs a comprehensive set of wage
data that clearly indicate the point of time when each wage rate has been set and for how
long it has been valid. For this purpose we have been able to construct a unique dataset
on collectively bargained wages in Austria from 1980 to 2006 that comprises around 100
individual wage-setting units covering almost the complete national labor force. These
data are particularily apt for our question at hand since the process of Austrian wage-
setting shows a clear structure of staggering. Employers and employees in the metal sector
traditionally start their negotiations after the summer (“autumn bargaining round”) while
the wage-setters in other sectors follow until May of the following year. In order to study
the importance of reference norms the use of these data is even more interesting since it
is often argued that in Austria the metal sector acts as a wage leader for the following
negotiations. We can use our dataset to actually test for this “folk wisdom” and to
contrast it with other assumptions about the structure of reference norms.
To this end we construct different reference norms that follow the suggestions in the
literature. Our results indicate that reference norms are in fact an important factor
for Austrian wage settlements. By and large the coefficient of the reference norm is
slightly higher than the coefficient of forecasted inflation. Furthermore, our findings
clearly suggest that the wage rates of other units (the wage rate of the metal sector and/or
of all other wage settlements since the last negotiations) matter more than internal habits
(i.e. the own last settlement). Finally, we get strong indication of asymmetries and wage
leadership in Austrian wage-setting behavior. This conclusion is supported by direct
nested and non-nested statistical tests as well as by tests that are based on implications
of the theoretical model. It is also suggested by an analysis of the individual, wage-
unit specific coefficients that result from the estimation of a random coefficient model. In
particular, we find that the wage-leading sector reacts significantly stronger to the general
macroeconomic situation than the following sectors. The latter take the wage agreement
of the metal sector as a guideline and thus put less emphasis on macroeconomic data and
forecasts.
Our findings have a number of consequences concerning inflation persistence and real
wage rigidity. First, reference norms are an important factor in wage-setting and they
should be included in realistic and comprehensive dynamic macroeconomic models. The
10ECBWorking Paper Series No 1047April 2009
assumption of reference norms leads to similar reduced forms as the approaches that
assume backward-looking price-setters, while at the same time being more in line with
empirical evidence. Second, in order to get a complete picture about the sources and
consequences of nominal rigidities it is important to study the microstructure of wage-
setting. Economies that are characterized by differences in the importance of reference
norms between sectors will show less persistence than countries with a symmetric struc-
ture.3 Third, underlying differences in reference norms could also be responsible for the
observed cross-country differences in inflation persistence and wage rigidities (cf. Cec-
chetti and Debelle, 2006; Dickens et al., 2007).
The paper is organized as follows. In the next section we present a simple model with
staggered wages that allows for reference norms. In section 3 we describe our data on
collective wage-bargaining in Austria and we report the results of the empirical analyses.
Section 4 concludes.
2 A model with wage staggering and reference norms
2.1 The set-up
We use a variant of the Taylor (1980) model with staggered wage contracts that considers
the role of reference norms in wage-setting. The model assumes that the total workforce
is divided into two sectors of equal size where sector A negotiates the wage in periods
t = 0, 2, 4, ... while sector B negotiates in periods t = 1, 3, 5, .... All wage contracts are
fixed for two periods (where one period corresponds to half a year). The fixed length of
wage contracts captures a prevalent feature of wage-setting in many countries (see section
3.2 below) and seems more appropriate than the assumption of Calvo contracts. The
wage-setting equation (for the adjusting sector i) is assumed to take the following
form:
wit =
(1− μi
)wi
t + μirnit (1)
where wit is the “pure wage target” of wage-setters in sector i , rni
t stands for their reference
norm and μi is the relative weight of these two magnitudes. The pure wage target follows
the specification in Taylor (1980), i.e.:
wit = bpt + (1− b)Etpt+1 + γi (byt + (1− b)Etyt+1) (2)
3Carvalho (2005) and Dixon and Kara (2007) study the consequences of asymmetries in the contractlength on the amount of persistence in Taylor models.
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The pure wage target wit depends on the expected price level and the expected level of
real activity (or excess demand) during the duration of the contract. The expected price
level is given by (bpt + (1− b)Etpt+1), where pt is the price level in period t and b is the
relative weight of the two periods over which the contract is valid. Similarly, yt is the
measure of aggregate demand in period t and γi represents the degree of “real rigidity”
(cf. Ball and Romer, 1990). The higher is γi, the stronger the wage target wit reacts to
the conditions in the real economy and thus the smaller is the degree of real rigidity.4
If μi = 0 wage-setters do not have reference norms and the wage-setting equation
(1) coincides with the original formulation in Taylor (1980). For μi > 0, however, wage-
setting is assumed to be influenced by reference norms. This specification is based on the
observation that in their negotiations wage-setters typically also care about other nominal
variables in a direct fashion (and not only via their impact on current and future price
levels). The reasons for such a behavior can be manifold and various explanations have
been proposed in the literature that range from efficiency wage and relative wage models
(Fuhrer and Moore, 1995; Danthine and Kurmann, 2004; Ascari and Garcia, 2004) to
models with wage norms (Hall, 2005; Gertler and Trigari, 2006). Although these models
differ in their motivation and also in their particular specification they typically imply an
additional role for past wage rates. The wage-setting equation (1) is meant to capture
the common element of these different specifications.
For our benchmark model we use the straightforward assumption of “external norms”
(i.e. norms that refer to the wage in the other sector):
rnit = w−i
t = w−it−1, (3)
where (−i) stands for the other sector. Equation (3) thus says that wage-setters in sector
A look at the wage level in sector B (rnAt = wB
t = wBt−1) while wage-setters in sector B
look at the wage rate in sector A (rnBt+1 = wA
t+1 = wAt ). This is a reasonable specification
that is in line with the results from survey studies (e.g. Agell and Bennmarker, 2007).
Other reference norms will be discussed below. Note that for the extreme case with μi = 1
assumption (3) implies complete stickiness of wages (i.e. wit = wi
t−1 = wit−2).
4Taylor did not derive his wage-setting equation from “first principles” but he motivated it as being“simple and plausible” (Taylor, 1980, p. 4). It can be shown, however, that a system of equations thatis very similar to the ad-hoc specification of the Taylor model can be derived as the linearized solutionto a fully fledged intertemporal optimization model (see appendix A and Ascari, 2000; Huang and Liu,2002). In this case all the variables have to be interpreted as being percentage deviations around theirrespective steady states.
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Equations (1) to (3) describe the basic structure of wage-setting in our framework that
will underlie our empirical estimations. In the following we want to use this description
of wage-setting behavior in an otherwise standard dynamic model in order to show how
the existence of reference norms changes the persistence of inflation. To this end we have
to specify how the other endogenous variables are determined.
Prices are set as a mark-up over wages and the price level pt is thus given by the
average wage:
pt =1
2
(wA
t + wBt
)(4)
As in many versions of the Taylor model we also assume that aggregate demand yt
depends on nominal demand (or the money supply) mt and the price level pt.5 In partic-
ular:
yt = mt − pt (5)
In order to close the model we have to make an assumption about the determination
of monetary policy. Since we are primarily interested in how the amount of intrinsic
persistence changes across different wage-setting regimes this assumption is not crucial
and we thus use the simple specification that mt follows an autoregressive process:
mt = ρmt−1 + νt, (6)
where νt is an i.i.d. error term. This completes the description of the model.
2.2 The solution of the model
In appendix B we report the solution for the general case of the dynamic model with
μA �= μB, γA �= γB and b �= 12. We show that this solution can be written as:6
wit = λiw−i
t−1 + θimt (7)
As is shown in appendix B the root λi that captures the amount of intrinsic persistence
between periods can differ across the two sectors, i.e. λA �= λB. One can insert, however,
5This is done in Taylor’s original model (1980) and also in various later contributions to this topic(e.g., Chari et al., 2000; Karanassou and Snower, 2007). Other papers, especially in the context of the“New Keynesian Phillips Curve”, treat yt as an exogeneous forcing variable (e.g., Roberts, 1995; Galıand Gertler, 1999).
6Note that equation (7) is only valid for the periods where the wage in sector i is changed. In theother periods wages are fixed and it thus holds that wi
t+1 = wit.
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w−it−1 = λ−iwi
t−2 + θ−imt−1 into (7) to express the wage in sector i in dependence of its
own last wage wit−2, i.e.:
wit = λiλ−iwi
t−2 + θimt + λiθ−imt−1 (8)
The level of annual persistence (i.e. from t− 2 to t etc.) is thus the same in both sectors.
We denote this degree of annual persistence by Λ ≡ λAλB and we will use this measure
for the numerical examples in the following sections.
In a symmetric world the two sectors differ only with respect to the period of time in
which their wages are negotiated. In particular, this case is characterized by μA = μB = μ,
γA = γB = γ and b = 12. It is evident (and shown in appendix B) that in this situation
the autoregressive persistence measure λi is the same in both sectors, i.e. λA = λB = λ.
It can be calculated as:
λ =1 + γ + μ(1− γ)− 2
√γ(1− μ2) + μ2
(1− γ) (1− μ), (9)
which implies an annual persistence measure of Λ = λ2. In the absence of reference norms
(μ = 0) this model corresponds exactly to the formulation of the Taylor model that can
be typically found in the literature (e.g. Romer, 2006, chap 6; Ascari, 2003; Karanassou
and Snower, 2007). In particular, for μ = 0 (9) reduces to the well-known expression:
λ =1−√γ
1 +√
γ(10)
For both (9) and (10) it holds that λ decreases in γ (∂λ∂γ
< 0). The more strongly wages
react to excess demand (the lower real rigidities) the lower will be the degree of persistence.
We can use the expression in (10) to briefly discuss the inflation or output persistence
puzzle as it arises in the context of the Taylor model (cf. Fuhrer and Moore, 1995;
Chari et al., 2000). The basis of the problem is that in microfounded models γ is not
a free variable but rather depends on a number of structural parameters. In particular,
under certain assumption one can show (see appendix A) that γ = −ηCC+ηLL
1+θηLL, where θ
is the elasticity of substitution between different varieties of goods and ηcc and ηll are
the inverses of the intertemporal elasticity of substitution of consumption and of labor
supply, respectively. Standard numbers for these parameters are (cf. Ascari, 2000, Table
1 or Dixon and Kara, 2007): ηcc = −1, ηll = 3.5, θ = 6. These values imply a value for
the real rigidity of γ = 0.21. Using different acceptable parameter values (e.g. a higher
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elasticity of marginal consumption ηcc or a lower elasticity of labor supply ηll) would
suggest even higher values of γ = 0.3 or above.7 Using (10) this corresponds to a degree
of period-on-period persistence of λ = 0.382 (for γ = 0.2) and λ = 0.292 (for γ = 0.3)
and to a degree of annual persistence of Λ = 0.146 and Λ = 0.085, respectively. These
degrees of persistence appear, however, too low and to be in contradiction to the existing
empirical literature. In particular, empirical estimates typically show values for the degree
of annual persistence that are larger than 0.25 and often larger than 0.5 (see e.g. Jeanne,
1998). In a similar fashion Ascari (2003) “defines a significant degree of persistence to be
a value of λ of at least 0.5” (p. 526). We can use this benchmark value of λ = 0.5 or
(Λ = 0.25) in order to judge whether a model is successful in producing an empirically
plausible degree of persistence for values of γ that are in line with the standard structural
parameters (i.e. between γ = 0.2 and γ = 0.3).
In fact, the expression for λ in (9) indicates that the introduction of reference norms
increases the amount of intrinsic persistence considerably. This is illustrated in Figure 1
for the measure of annual persistence Λ. For both γ = 0.2 and γ = 0.3 an increase in the
importance of reference norms to values between μ = 0.2 and μ = 0.5 is sufficient to in-
crease Λ to levels that are in line with the empirically observed degree of persistence. Note
also that limμ→1
λ = 1. This means that under the assumption of external reference norms
(cf. (3)) we can have complete persistence (λ = 1) if comparisons play an overwhelming
role in wage-setting.
Insert Figure 1 about here
2.3 The role of different reference norms
We have seen in the last subsection that the introduction of reference norms can increase
inflation persistence considerably. In this and in the next subsection we want to study
how this impact changes once we allow for different references norms and for possible
asymmetries between sectors in the importance of reference norms.
In the benchmark specification (3) we have assumed that wage-setters have backward-
looking external reference norms. In the related literature, one can however find a number
of different assumptions concerning the variable(s) that primarily influence wage-setting
7The assumption of decreasing returns to scale in production (α < 1) does not change the main
message. In particular, in this case we get that (see Ascari, 2003): γ =−ηcc+
1θ(1−α)+α
ηll
1+ θθ(1−α)+α
ηll. Using α = 2
3
and again ηcc = −1, ηll = 3.5 and θ = 6 we get γ = 0.26. In a model with staggered price-setting Chariet al. (2000) get a value for γ that is even larger than 1 (since they have γ = ηll − ηcc).
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decisions (see Agell and Bennmarker, 2007; Danthine and Kurmann, 2006). The choice
of the reference norm can evidently have an important impact on inflation persistence.
The most direct way to see this is if we assume that instead of (3) wage-setters only
make contemporaneous comparisons, i.e.
rnit = wi
t (11)
Inserting this assumption into (1) implies that wit = wi
t and we are back to the model
without reference norms. In general, the impact of the reference norm on the stickiness of
wages will depend on the degree of “backward-lookingness” and on the extent to which
they are directed to the other sector. We want to illustrate this by using two alternatives to
the external norm that are discussed in the literature. For the first alternative specification
we assume a “price indexation norm” where reference norms are given by the actual
price (or wage) level. This corresponds to an assumption that is frequently made in the
related DSGE literature (cf. Christiano et al., 2005; Smets and Wouters, 2007). In these
papers it is assumed that wages that are not optimally chosen in a certain period are
simply indexed to the past or current rate of inflation. Transformed from growth rates to
levels and translated into the model with reference norms this can be expressed as:
rnit = pt (12)
For the second alternative we assume that wage-setters have “habits”, i.e. their reference
norm consists of the last increase of their own wage. This “habit-persistence norm” is
thus given by:
rnit = wi
t−2 (13)
In Table 1 we compare the degrees of inflation persistence for the three alternative ref-
erence norms and for different parameter values for γ and μ. The numbers in the table
correspond to the measure of annual persistence Λ since this allows for better compar-
isons once asymmetries between sectors are taken into account. For the habit persistence
norm the solution cannot be expressed in an AR(1) form as in (7) and in this case the
persistence measure corresponds to the sum of the first two lags.8
8One can think of many other possible reference norms. E.g., one could specify rnit in such a way that
it corresponds to the model by Fuhrer and Moore (1995) or to the alternative version of their model inHolden and Driscoll (2003). Also one could use a “forward-looking external norm” where wage setters takeinto account that the norm will be present today and in the next period (i.e. rni
t = bw−it +(1−b)Etw
−it+1).
We stick here to the alternative norms (12) and (13) since they are most frequently discussed in the
16ECBWorking Paper Series No 1047April 2009
Insert Table 1 about here
We observe that inflation persistence is lower for the price indexation norm and higher
for the habit persistence norm. We have, e.g., that for γ = 0.2 and μ = 0.5 the parameter
Λ is 0.702 for the case of the external norm while it is only 0.539 for the price indexation
norm but 0.916 for the habit persistence norm. For the price indexation norm this follows
from the fact that the norm pt now includes not only the past wages of the other sector
w−it−1 but also wages wi
t that are set in the own sector in the current period and thus include
already a reaction to the current economic situation. Persistence is higher for the habit
persistence norm than for the external norm since in this case there is no cross-sectional
interaction in reference norms and this increases the amount of sluggishness. These results
imply that, not surprisingly, the type of reference norm can have a significant impact on
the degree of persistence. This is potentially important since differences in reference norms
seem to be a real-world phenomenon. In fact, Agell and Bennmarker (2007) document
considerable differences in reference norms between Sweden and the US where external
norms are found to play a larger role for Swedish firms.9
2.4 Asymmetries in the importance of reference norms
The case of asymmetric importance of reference norms is also highly relevant since it
captures the argument that there exist differences in the behavior of wage-setters across
sectors. A particularly important example for such asymmetries is the case of wage
leadership. In the language of our model this would mean that the wage setters in both
sectors have external reference norms while μB > μA (if sector A is the wage leader) and
possibly μA = 0. In Table 2 we report the values of Λ for two levels of γ (γ = 0.2 and
γ = 0.3) and for different assumptions about the importance and possible asymmetries
in external reference norms. In particular, we denote by μ the average importance of
reference norms in the economy, i.e. μ = 12
(μA + μB
). In the first column we show the
results for μ = 0 and in the second block of columns the results for μ = 0.5 (both for a
symmetric case with μA = μB = 0.5 and an asymmetric one with μA = 0 and μB = 1).
Insert Table 2 about here
literature.9They explain this finding in the following way: “The precision of the information about external pay
appears to be higher among workers in unionized firms” (Agell and Bennmarker, 2007, p. 363).
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Table 2 shows that an increase in the importance of reference norms from μ = 0 to
μ = 0.5 increases Λ from 0.146 to 0.702 (for γ = 0.2). If there are, however, asymmetries
in reference norms (μA = 0 and μB = 1) then Λ is significantly lower at 0.5. This drop in
Λ is even larger for γ = 0.3 where the increase in Λ from 0.085 (for μ = 0) to 0.602 (for
μ = 0.5) is almost halved (to Λ = 0.368) for the case of asymmetric reference norms.
The results of Table 2 indicate that it is important to know if wage-setting is char-
acterized by asymmetries, e.g. by an outright system of wage leadership. In the latter
case, corporatist countries with a clear pattern of staggered wage-setting might still face
a rather low level of persistence (even if the average importance of reference norms is
large). This phenomenon could thus be partly responsible for the fact that different coun-
tries with apparently quite similar labor market institutions show considerably different
degrees of inflation persistence (cf. Cecchetti and Debelle, 2006).
So far we have assumed that the degree of real rigidity γi is identical in the two
sectors. If this is not the case then it can be shown that a sufficient condition for a system
with wage leadership to have less persistence than a symmetric system is that the degree
of real rigidity in the leading sector is smaller than the one in the following sector (i.e.
γA > γB). This conforms to the often heard argument that a stable system of wage
leadership presupposes that the wage leader is situated in a competitive segment of the
economy and not, e.g., in the public sector.
An additional source of asymmetry is the potential clustering of wage contracts. In
the empirical dataset that we are going to use later we see, e.g., that almost 50% of
all new wage agreements take effect in the months January to March. This clustering
can have important implications for the transmission of monetary policy (cf. Olivei and
Tenreyro, 2007). For the question at hand, however, the effects are rather muted. Under
the assumption that sector A subsumes only 10% of all firms (and γ = 0.3) the persistence
measure Λ can be calculated as: 0.034 (for μ = 0), 0.601 (for μ = 0.5) and 0.372 (for
μ = 0 and μA = 0). These figures are close to the results for the case with symmetric
sector sizes.
On the whole we can conclude that both the specific nature of the reference norms
and asymmetries in the importance of the norms matter for the persistence of inflation.
18ECBWorking Paper Series No 1047April 2009
3 Empirical Part
In order to empirically test the interplay between staggered wages and reference norms
one needs a particular set of wage data that include information about the actual time of
wage changes. We have been able to construct such a dataset that is based on collectively
bargained wages in Austria. We use this dataset in the following to investigate the role
of reference norms in an economy with a clear structure of wage staggering. We want to
answer three questions: First, do wage-setters have reference norms or is their behavior
only influenced by expectations about prices and aggregate demand as assumed in the
standard model? Second, if reference norms do play a role, can we determine which
formulation of reference norms is most appropriate? Third, is their any indication of
asymmetries in wage-setting behavior (“wage leadership”)?
3.1 Estimation Equation
The main equation for estimation follows directly from equation (1). If we take the first
difference of equation (1) together with (2) we get (for b = 12):
Δwit = (1− μi)
1
2
{Δpt + EtΔpt+1 + γi (Δyt + EtΔyt+1)
}+ μiΔrni
t + (14)
(1− μi)1
2
{(pt − Et−1pt) + γi (yt − Et−1yt)
}
Equation (14) states that wage growth in sector i will depend on expected inflation and
expected changes in real activity over the duration of the contract. The expressions
in the second line of (14) are expectational errors that should be zero on average if
people form rational expectations (see Roberts, 1995). We can generalize this equation
to a model with monthly staggering. In order to distinguish clearly between a year τ
and a month j we denote with wij,τ the wage that is set by the wage-setting unit i in
month j in year τ . We denote by Δpj,τ the rate of inflation over the upcoming year
starting in month j. This means, e.g., that Δp1,τ = 112
(Δp1,τ + Δp2,τ + ... + Δp12,τ ),
Δp2,τ = 112
(Δp2,τ + ... + Δp12,τ + Δp1,τ+1) etc., where Δpj,τ = (pj,τ − pj,τ−1). In a similar
fashion we denote the change in real activity over the next year by Δyj,τ . Our estimation
equation takes the following form:
Δwij,τ = βi
0 + βi1Ej,τΔpj,τ + βi
2Ej,τΔyj,τ + βi3Δrni
j,τ +(δi)′
Xij,τ + εi
j,τ , (15)
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where βi0 is an individual effect and Xi
j,τ is a vector of additional (possibly wage-unit-
specific) regressors that might have an impact on individual wage growth and that are
used in some of the following specifications. These additional regressors include, e.g.,
expectational error terms, time dummies and measures for the length of the wage contract.
We have also introduced an error term εij,τ which may include sectoral or aggregate shocks.
As written in equation (15), the empirical specification allows for possible heterogeneous
reactions across wage-setting units. This refers not only to the constant βi0 as in normal
fixed or random effects models but also to the slope coefficients βi1 to βi
3 and (δi)′.
Furthermore, it is important to note that the theoretical model makes strong pre-
dictions about the size of the coefficients. Most importantly, the model implies that
βi1 = (1− μi) and βi
3 = μi and that a correct empirical specification should thus be con-
sistent with the condition that βi1 + βi
3 = 1. The close connection between the theoretical
model and the estimation equation is thus quite helpful in analyzing and interpreting the
results. In order to directly test the wage-setting equation (15) we have to find data for
the main variables Δwij,τ , Δpj,τ , Δyj,τ , and Δrni
j,τ . We will describe our data sources after
giving a short overview of some specificities of the Austrian system of wage bargaining.
3.2 The Austrian system of collective wage bargaining
Wage determination in Austria is strongly dominated by a system of collective bargain-
ing.10 On the side of the employees there is a peak organization, the Austrian Federation
of Trade Unions, to which the individual trade unions are attached. These individual
trade unions are mainly organized along sectoral and occupational dimensions. On the
side of the employers there is also a central organization, the Austrian Federal Economic
Chamber, which covers basically all private companies. Collective bargaining mainly takes
place at the sectoral and industry level and regional differences in wage agreements do
not play an important role. Although collective bargaining is in principle confined to the
private sector there is also an influential public sector union that negotiates over wages
with representatives of the government. The coverage rate of the collective agreements is
very high (around 95%). At the moment around 400 collective agreements are signed each
year of which around 250 are national agreements. Many of these agreements, however,
refer only to a small number of employees while around 20 large agreements together cover
more than half of the complete labor force. Since the beginning of the 1980s the annual
bargaining process follows a similar pattern where the metalworking industry starts the
10Details can be found in Traxler et al. (2001).
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round of negotiations in September or October (“autumn bargaining round”). Since 1984
the collective agreement in this sector (which covers about 11% of the total wage bill)
always takes effect in November. The other wage-setting units follow the metal sector in
a staggered fashion. The collective agreement of the wholesale and retail trade sector that
also represents a large part of the labor force (around 13%) normally becomes effective
in January as is the case for the public sector. Finally, a number of important sectors
typically have their wages only set in May (this is true, e.g., for construction and parts of
the chemical and tourism sector which together cover around 10% of the wage bill).
3.3 The data
3.3.1 Collective wage agreements
Unfortunately, there does not exist an accessible complete database for all collective wage
agreements in Austria. There exists, however, an “index of agreed minimum wages” that
subsumes data for a large number of disaggregated wage-setting units that are mostly
organized along sectoral lines. We use these disaggregated series to construct an annual
dataset that contains for each included wage-setting unit i the annual increase in the
collectively bargained wage Δwij,τ , the month in which this agreement came into effect
and the duration until the next agreement is reached. We have to exclude some units
either because we do not have data over the whole time span or because they refer to
quite heterogeneous sectors with rather erratic patterns (e.g. many small changes each
year). This leaves us with a number of 100 individual times series for collectively bargained
wages comprising 92% of the total database. We focus on the time period from 1980 to
2006. Table 3 summarizes these data.11 One sees that most contracts are signed in winter
or spring (January to June). In fall only around 10% of new agreements are concluded
but these include the important agreement of the potentially wage-leading metal sector.
Most wage agreements (> 80%) are valid for exactly one year.
Insert Table 3 about here
Our data on disaggregated wages have two potential drawbacks. First, the available
data only indicate when a new collective agreement became effective and not when the
change was negotiated. It could in principle be the case that there is a longer time lag
between a wage increase and the time when it has been scheduled. For the estimation of
11In appendix C we provide more details on the construction of our dataset.
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equation (15) it is important to know on which macroeconomic forecasts the wage-setters
could have based their decisions. Casual observations as well as personal information by
involved experts suggest, however, that the time lags between the end of the negotiations
and the implementation are rather short. Second, the available time series only report
the collectively bargained increase in the minimum wage for each unit. As in many
other countries, in Austria effective wages are often higher than these agreement-specific
minimum wages. Although this is admittedly a handicap of the dataset it is probably less
severe than one could expect. The increase in effective wages which are also negotiated
in some industries is mostly parallel to the increase in minimum wages. Furthermore,
the development of the collective wage index follows closely the one of the comprehensive
variable “compensation per employee for the total economy” from national accounts.
3.3.2 Macroeconomic forecasts and forecast errors
For the expected values Ej,τΔpj,τ and Ej,τΔyj,τ in (15) we use the quarterly forecasts
of the Austrian Institute of Economic Research (WIFO). This institute has a long tra-
dition in forecasting the future path of the Austrian economy and its results are widely
published in the media and are also the “official” numbers that are used in the collective
wage negotiations. The forecasts are typically published in March, June, September and
December each year and they include forecasts for the current and the next year for a
number of macroeconomic variables. We use the figures for the growth rate of GDP, for
the rate of inflation and for the unemployment rate. In order to match these forecasts
with the time series of collectively bargained wages we assume that wages that come into
effect in a certain month are based on the most recent forecasts available in the previous
month.12 The expected development of a variable over the duration of the wage contract
is calculated as the weighted average of the forecasts for the current and for the next
year.13
As far as the variable for real activity Ej,τΔyj,τ is concerned there exists a long dis-
cussion on which is the most appropriate way to measure it (cf. Roberts, 1995; Galı and
Gertler, 1999; Rudd and Whelan, 2006). In the related literature one can find specifica-
tions that use — among others — the output gap, real marginal costs, the labor share
12So strictly speaking, the information set of expectations formed in month j contains only informationthat was available at the end of month j − 1.
13So we assume, e.g., that the wage agreement that became effective in May 2002 is based on anexpected rate of inflation that is calculated as 8/12 of the WIFO-March-2002 forecast for the currentyear plus 4/12 of WIFO-March-2002 forecast for the next year. For details see appendix C.
22ECBWorking Paper Series No 1047April 2009
and the unemployment rate. Due to problems with data availability we base our estima-
tions on forecasts of GDP growth and the change in the unemployment rate. The first is
an appropriate measure for real activity as it is closely related to changes in the output
gap. The use of the change in the unemployment rate as a measure for business cycle
conditions can be motivated by Okun’s law as noted by Roberts (1995).
In some of our estimations we also use forecast errors as suggested by the theory that
leads to the empirical specification in (15). The forecast error of a variable is measured
as the difference between the realized and the expected value. For some of our robustness
tests we will also use different macroeconomic aggregates (e.g. lagged instead of forecasted
values). In all cases where we do not have monthly variables we interpolate them in the
same way as it is done in the construction of monthly series for the forecasts.
3.3.3 Reference norms
We use 4 reference norms that have been discussed in section 2:
• External reference norms (“external norms”): For each wage-setting unit the
reference norm is given by the (weighted) average increase of wages in all other
units that could be observed since the last time that its own wage level had been
changed.
• Wage leadership reference norms (“leadership norms”): Each wage-setting unit
takes the wage increase in the metal sector as its reference norm. The wage-setters
in the metal sector do not have reference norms. There are 14 wage-setting units
which typically contract in November. We have subsumed 4 of these units into the
category “wage-leader” since all of these units are attached to the metal sector,
negotiate together and have reached almost perfectly correlated wage agreements.
The remaining 10 wage-setting units in November include, e.g., units in the chemical
and the paper industry.
• Habit reference norms (“habit norms”): Each wage-setting unit regards its own
last wage change as the reference norm.
• Price indexation norms (“indexation norms”): All wage-setting units take the
average inflation rate over the last year as their reference norm. This could be a
reasonable assumption if, e.g., unemployment benefits are indexed to changes in the
price level.
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3.4 Empirical Strategy
It is not straightforward to say which reference norm is the correct assumption. The
results of the survey studies indicate that various reference norms might be important.
Furthermore, some of the norms are clearly not independent of each other. For example,
even if all wage-units have a leadership norm the external norm will also show a significant
influence due to the staggered structure of wage agreements. Therefore we will not a priori
limit ourselves to a single norm but rather try to find out empirically which norm provides
the best description of the data.
The choice of the right empirical specification to test our main hypotheses involves
a number of issues. The most important one is related to the question whether it is
reasonable to assume that all wage-setting units react to the macroeconomic variables
and the reference norms in the same fashion. In fact, our theoretical model suggests
that there might be differences in the weight of the importance of reference norms μi
and possibly also in the degree of real rigidity γi. These differences should be reflected
in heterogeneous regression coefficients as written in equation (15).14 In order to allow
for this possible heterogeneity we will estimate our benchmark equation not only with
the usual homogeneous coefficients techniques (i.e. with fixed effects [FE] and random
effects [RE] models) but also with two varying-coefficients estimation methods that can
be frequently found in the literature: the random coefficients (RC) model by Swamy
(1970) and the mean group (MG) estimator suggested by Pesaran and Smith (1995). A
discussion of these methods can be found in Hsiao (2003, chap. 6) and in Hsiao and
Pesaran (2004). The basic difference between the RC and the MG estimator is related
to their assumption about the nature of heterogeneity. The MG estimator is based on
the assumption that deviations from the mean coefficient are deterministic while the RC
estimator assumes that they are stochastic. Accordingly, the MG estimator is defined as
the simple average of individual OLS estimates while the RC estimator uses a weighted
average of these estimates where the optimal weights are inversely proportional to the
covariance matrices. Hsiao and Pesaran (2004) show that the two estimators are equivalent
if the number of time periods is sufficiently large. As we will see below, our data strongly
reject the assumption of homogeneous coefficients and we will mostly work with the RC
specification.
A second specification issue concerns the treatment of possible common trends in
14This is confirmed in a different context by the results in Imbs et al. (2007) who show that homogeneityin pricing behavior is strongly rejected for French data.
24ECBWorking Paper Series No 1047April 2009
the data (like a general decrease in the rate of inflation). This could suggest the use
of annual time dummies or of other variables that capture these time trends. It is,
however, not clear whether this is appropriate for our research question since general time
trends in unit-specific wage growth should already be captured by the movements in the
nominal variables on the right hand side of the wage-setting equation. Also, in the case of
specifications with heterogeneous slope coefficients the inclusion of annual time dummies
would be impossible. In order to allow for some broad changes in wage-setting over time
the specifications include decade time dummies.15
Our analysis involves three steps. First, we will compare the average estimated coef-
ficients and we will investigate whether and for which reference norm the theory-based
condition β1 + β3 = 1 is satisfied.16 In a second step we conduct a number of nested and
non-nested statistical tests in order to determine which norm gives the most consistent
results. Finally, we also use the individual, wage-unit-specific estimates from the RC
specification. We look again at the above-mentioned condition concerning the coefficients
of expected inflation and reference norms that should also be valid on an individual basis.
Furthermore, we will also argue that neither theory nor the actual wage-setting practice
in Austria suggest that the individual coefficients should contain a systematic temporal
pattern. This fact can also be used to decide about the appropriateness of different ref-
erence norms specification. Our overall result is that the leadership norm performs best
under all of the employed tests.
3.5 Main results
Tables 4a and 4b present the results of estimating equation (15) with a FE, a RE, a
RC and a MG specification. In Table 4a we use the external norm as our measure of
reference norms while in Table 4b we use the leadership norm. Furthermore, in both
tables we investigate the impact of either GDP growth or the change in unemployment
as the measure for real activity.
Insert Tables 4a and 4b about here
Looking at Tables 4a and 4b we can make the following observations:
15I.e. for 1980–1989, 1990–1999 etc. In robustness tests we have also employed 5 year dummies or alinear time trend. The main results are not affected by these changes.
16We write βk for the estimated cross-sectional average of the individual coefficients βik.
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• The differences between the four specifications are rather modest for the estimations
with external norms and larger for the ones with the leadership norm. As far as
the homogeneous coefficient models are concerned for both specifications the data
suggest a FE model. It is important to note, however, that a thorough discussion
of the case with homogeneous coefficients is rather superfluous since for both norms
the results indicate that there is a considerable degree of heterogeneity in the
parameter estimations. At the bottom of the tables we report the test statistics for
parameter constancy that has been suggested by Swamy (1970) for the RC model.17
The null hypothesis of homogeneity of coefficients is strongly rejected for all 4 RC
specifications in Tables 4a and 4b. Tests based on the individual estimates under-
lying the MG estimator also show considerable and significant differences between
wage-setting units. In light of these results, we will maintain the assumption of
heterogeneous coefficients and we will employ the RC model in the following as our
benchmark estimation method.
• Reference norms are an important factor for the determination of wages. The
coefficient for the reference norm is highly statistically significant in all specifications
and its size is considerable, typically between 0.5 and 0.6. The theoretical model
of section 2 suggests that an importance of reference norms in the neighborhood of
μ = 0.5 is sufficient to create reasonable degrees of inflation persistence (cf. Figure
1 for the symmetric case).
• The expected rate of inflation over the duration of the contract (Ej,τΔpj,τ ), on
the other hand, is also an important factor for negotiated wage rates as suggested by
New Keynesian theories. Its influence appears to be slightly lower than the influence
of reference norms. As described above, the theoretical model underlying equation
(15) implies that the (average) estimated coefficients of expected inflation β1 and
reference norm β3 should sum up to 1. In Tables 4a and 4b we report the sum of
these two coefficients in the lower part of the tables and we also give the statistics
and the p-value for the corresponding F-tests. We get a striking result. The null-
hypothesis implied by the theoretical model is never rejected for the models with
heterogeneous coefficients (RC or MG) and the use of leadership norms (columns (3),
(4), (7) and (8) in Table 4b), while it is always rejected in the remaining cases with
external norms (Table 4a) and with the use of homogeneous coefficients (columns
17This statistic is distributed χ2 with k(P − 1) degrees of freedom where P is the number of groups(100 in our case) and k is the number of different parameters (6 in our case).
26ECBWorking Paper Series No 1047April 2009
(1) (2), (5) and (6) in Table 4b). These results thus also suggest the use of a model
with heterogeneous coefficients and they furthermore give a first strong indication
that the leadership norm is probably a more accurate concept than the external
measure.
• The expected development of real activity contributes to the size of the wage
increase. If GDP is expected to grow faster by 1% this will increase the average
wage agreement by between 0.08% and 0.33%. On the other hand, if unemployment
rate is expected to decrease by 1 percentage point this is expected to boost wage
claims by between 0.22% and 1.23%. Interestingly, these different values for GDP
growth and the change in unemployment imply an Okun coefficient of about 4
which is broadly compatible with empirical estimations for Austria. An interesting
result that is crucial for our argument is related to the fact that the coefficient
of expected inflation is lower and the coefficient of expected real activity much
lower for the leadership norm. This result is directly compatible with the wage
leadership story where it can be assumed that the wage-leaders in the metal sector
look closely and thoroughly at the macroeconomic variables. The other wage-setters
that follow, however, orient themselves primarily on the result on the metal sector.
Partly, because they lack the resources to engage in time-consuming forecasts and
partly because they trust the accurateness of the general assessment in the wage-
leading sector. As a result, the broad macroeconomic outlook is already contained
in the leadership norm and over and above this norm there is little influence on the
negotiated wages.
3.6 Nested and non-nested tests on the importance of reference
norms
In Tables 4a and 4b we have only focused on two commonly used reference norms. In
this section we will also look at the two other norms that correspond to proposals in the
related literature: the habit norm and the price indexation norm. We want to use formal
statistical tests to investigate in a more systematic way which one of the four norms is
the most appropriate concept. It is, however, quite difficult to distinguish between the
alternative formulations since most of them are highly correlated. It is therefore not
surprising that if we estimate the benchmark equations in Table 4a and 4b with the
two alternative norms (results not shown) they also come out with a significant positive
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coefficient. It is, however, important to note that also for these alternative concepts (as
was the case for the external norm) the condition that β1 + β3 = 1 can be rejected for all
specifications.
In order to get an idea about the relative importance of the different norms we first use
non-nested J-tests (cf. Smith, 1996; Greene, 2003, chap. 8): We regress the dependent
variable Δwij,τ on the benchmark set of regressors including the change in reference norm
Δrn1,ij,τ . The fitted values of this regression are then included in a regression of Δwi
j,τ on
the benchmark variables plus an alternative norm Δrn2,ij,τ . If Δrn2 is the correct measure
then the coefficient on the fitted values from the first regression should be close to zero
(which is determined by a t-test). In a next step we reverse the roles of Δrn1 and Δrn2.
Unfortunately, this test does not guarantee unambiguous results since it is possible that
we reject an independent role of Δrn1 in the first and of Δrn2 in the second regression.
In Table 5 we report the results of the J-tests. We follow the practice of Smith (1996)
and interpret the relative size of the t-statistics as an indicator of “dominance” in order
to deal with the inconclusive cases. Overall, the results in Table 5 suggest that the
leadership norm is the most consistent and important measure of reference norms. It is
the dominant measure in all pairwise comparisons and in the case of the price indexation
norm the alternative measure is not even statistically significant. The external norm is
also an influential measure that is dominant in all regressions except the one where it is
paired with the leadership norm.
Insert Table 5 about here
Similar conclusions also result from nested tests in which all pairwise combinations of
reference norms are included at the same time into the benchmark estimation. This is
shown in Table 6. Although collinearity is likely to affect the estimates, the coefficient
on the leadership norm always stays significant and also its variation in size is rather
small. The external norm, on the other hand, becomes much smaller (although still
statistically significant) once entered together with the leadership norm while it seems to
be rather stable in the other comparisons. The coefficients on the habit norm and the
price indexation norm are rather small and often insignificant.
Insert Table 6 about here
On balance, these results suggest that the leadership norm seems to be the most
appropriate description of the reference norm that influences the process of wage-setting
in Austria. This conforms with the results based on the condition that β1 + β3 = 1.
28ECBWorking Paper Series No 1047April 2009
3.7 An analysis of the individual heterogeneous coefficients
So far we have focused our analysis on the average values of the empirical models with
heterogeneous coefficients. For our purpose it is, however, also useful to look at the
individual coefficients that underlie these common measures. An analysis along these
lines can deliver important insights into the nature of reference norms and the temporal
and possibly asymmetric structure of wage-setting.
The first step in this context is to look again at the implication of the theoretical
model. The condition that the coefficients of the reference norm and of expected inflation
should sum up to 1 is supposed to hold not only in the aggregate but also for each of the
100 wage-setting units individually. We have conducted F-tests using the results from
the individual estimations that underlie the RC specification. In Table 7 we report the
percentage of wage-setting units for which the individual F-tests imply a rejection of the
condition for various assumptions about the nature of reference norms. For the case of
leadership norms the theoretical implication is rejected for 15 of the 100 wage-setting
units (using a 5% level of significance; for the 1% level the condition is violated in only
6% of the cases). The rejection rate is much higher for the external, the habit and the
price indexation norm where it comes out as 69%, 89% and 27%, respectively. Also for
the case where we abstract from reference norms, the individual coefficients of expected
inflation (which is now the only nominal variable on the right-hand-side of the wage-
setting equation) are in 23% of the units significantly larger than unity.18 The F-tests
based on the individual coefficient estimations thus again confirm the conclusions based
on the average coefficients and on the nested and non-nested tests.
Insert Table 7 about here
The individual coefficients can, however, also be used to provide further evidence
on the appropriateness of the different reference norms. This argument is based on an
analysis of the temporal pattern of the reaction to the macroeconomic variables and the
reference norm. In particular, we can order the individual regression coefficients βi1 to βi
3
with respect to the (median) month in which each of the 100 wage-setting units typically
concludes its wage agreements. A-priori there exists no reason to believe that there should
be any discernible temporal pattern in the size of these coefficients (e.g. that they should
be higher in spring than in fall or vice versa). In fact, if the assumption of complete
18Note that in this case the F-test on the common-mean coefficient of expected inflation also rejectsthe null-hypothesis of a value of 1.
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symmetry in wage-setting is valid (as assumed in the model of section 2.2) then the
coefficients should be identical across wage-setting units. All possible differences in the
estimated coefficients should then only be due to measurement or random errors and thus
should not show any noticeable temporal structure. In Figure 2 we present pictures that
allow to analyze this topic in more detail for the case without norms (panel A), with
external norms (panel B) and with leadership norms (panel C). For each norm we show
the size of βi3 and of βi
2.19
Insert Figure 2 about here
We start our discussion with the case that abstracts from reference norms and that
corresponds to the standard wage-setting equation in New-Keynesian models. The pic-
tures in panel A of Figure 2 give an unambiguous and striking result. There seems to be a
clear temporal pattern in βi2, i.e. in the reaction to expected changes in the unemployment
rate. It is strongest for the sector that negotiates in November and afterwards decreases
in importance. In fact, the average coefficient for the units contracting in November
(−1.84) is more than double the size than for the rest of the economy (−0.74). This is in
itself a strong indication that the November agreements play a special role in the system
of wage-setting in Austria and that there seem to be noticeable asymmetries across sec-
tors.20 The wage leading units apparently put a considerably higher weight on the general
macroeconomic situation as reflected by their expectations about future unemployment.
If we look at the distribution of the individual coefficients when external norms are used
(panel B of Figure 2) we find a similar picture. In this case the RC model reveals again a
clear temporal pattern where the importance of reference norms seems to increase over the
year starting in November while the (absolute values of the) coefficients of unemployment
decrease from November to the summer of next year. The assumption of symmetric
reference norms is thus again contradicted by the data.
If we repeat the same exercise for the leadership norm we find different results as shown
in panel C of Figure 2. There is no discernible temporal pattern in the importance of
19The individual coefficients shown in the figures are the ones from the RC estimation. Here we had todeal with an issue that arises in the empirical estimations. Since the leadership norm is zero for the fourwage-leading units their values are dropped from the RC estimation altogether and we would not haveresults for these crucial units. In order to prevent this from happening we have set for these 4 units theleadership norm equal to 1 in the year 1980. This amounts to an additional year dummy for these fourunits that is, however, not statistically significant and leaves all coefficients for the other units virtuallyunchanged. Moreover, the use of the individual OLS regressions that underlie the mean group estimatorleads to completely parallel results.
20There are 14 units that typically contract in November, from which we have categorized 4 as thewage leaders. The average coefficient for the wage-leaders is −2.08.
30ECBWorking Paper Series No 1047April 2009
reference norms anymore. Their average value is almost identical for the sectors following
the agreements in November. The same is also true for the estimated reaction to expected
changes in unemployment (βi2) where the temporal pattern is weak (or basically non-
existing). The four units that comprise our group of wage leaders show the highest
reaction to changes in the unemployment rate (between −1.99 and −2.2) while the other
10 units that contract in November reveal a reaction that is more similar to the rest of the
economy except two units (white collar employees in the chemical and the paper industry
for which the estimated coefficient is around −1.3). This suggests that these other units
already have information about the negotiated wage in the metal sector and use this as a
guideline for their own wage agreements.
The results taken together imply that the assumption of symmetric reference norms
is not appropriate for the Austrian situation. One possible explanation for the observed
temporal patterns in the case of external or non-existing norms could be that wage-
setting units are in fact ordered over the year with respect to the strength with which
they react to the macroeconomic situation. An inspection of the nature of the 100 units
does not support this hypothesis, however, since the units that contract later in the
year include a number of sectors that are typically assumed to react rather strongly to
business cycle conditions (like, e.g., the construction sector which contracts in May).
Also the increasing temporal pattern of the coefficients of reference norms βi3 is rather
implausible and contradicts anecdotal evidence that — if anything — the importance of
norms should decrease over the course of a wage round (see Traxler et al., 2008). On the
whole, we would thus argue that it is more suggesting to interpret the observable temporal
patterns in the estimations that use no or external reference norms as an indication of
misspecifications of the empirical relation.
The results of this section therefore further support our overall conclusion that wage-
setting in Austria is characterized by a system of wage leadership by the metal sector. In
the negotiations of fall (“autumn bargaining round”) the wage leader mostly focuses on
the macroeconomic conditions that are expected to prevail in the upcoming year and puts
no (or at least much less) weight on the wage rates that have been set in the negotiation
rounds that ended before summer. This is different for the wage agreements following
the metal sector that seem to regard these earlier settlements as a benchmark that acts
as a reference point for the success of their own wage agreements.21 The fact that the
21The results on wage leadership confirm parallel findings by Traxler et al. (2008) who work with asimilar dataset on collectively bargained wages in Austria and also conclude that the metal sector actsas the wage leader. Their approach to the topic is, however, more from the perspective of industrial
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wage leader is mostly concerned with the general macroeconomic environment and less
with wage comparisons is likely to contribute to a system that shows less endogenous
persistence than in other countries.
3.8 Further Robustness Tests
So far we have used a rather parsimonious specification to study the role of reference
norms in wage-setting. In this section we want to check the robustness of our benchmark
estimations with leadership norms by using different samples and including additional
regressors. In Table 8 we present the results when the expected change in the unem-
ployment rate is used as the measure for real activity. The results (not shown) for GDP
growth as a measure of real activity are similar.
Insert Table 8 about here
In columns (2) and (3) of Table 8 we look at the benchmark estimation for two dif-
ferent time samples (before and after 1993). The results are fairly similar although the
coefficient of the reference norm is smaller and the one of expected inflation is higher
for the later sample. This would suggest that after the middle of the 90ies the rate of
inflation has become a more important anchor for wage-setting than it has been the case
before. One would speculate that this might be at least partly connected to the influence
of European monetary integration and to the “Great Moderation” in general. If we focus
only on the private sector (79 instead of 100 wage-setting units) the main results are also
unchanged (see column (4)). As expected, the private sector seems to react more sensi-
tively to business cycle conditions although the difference is not statistically significant.
In column (5) we have pooled similar wage-setting units together (i.e. units in identical
sectors that negotiate at the same time of the year and reach very similar agreements).
This leaves us with 55 “independent” instead of the 100 total units. Using these inde-
pendent units strengthens the role of wage leadership since the coefficient of the reference
norm increases (to 0.63) and the coefficient of the change in unemployment decreases and
becomes insignificant.
relations and they provide more detailed evidence on the emergence of this system around 1980 and onthe specific role played by employer organisations and unions. In contrast to their work, we derive theestimation equation from an explicit theoretical model, we focus on the implications of asymmetries inreference norms on inflation persistence, we use explicit forecasts for the macroeconomic variables andwe also consider alternative hypotheses concerning reference norms.
32ECBWorking Paper Series No 1047April 2009
In column (6) we include forecast errors as suggested by the theory-based formulation
in (15). This considerably increases the role of expected real activity but leaves the
coefficients of all other variables basically unchanged. Also the coefficients of the forecast
errors themselves are not statistically significant which can be regarded as a confirmation
of the assumption of rational expectations.
In column (7) we include lagged inflation in the benchmark equation. This corresponds
to a “hybrid” Phillips curve that is quite popular in the recent macroeconomic literature.
The results are almost unchanged and the coefficient of past inflation is almost zero,
thereby confirming that the reference norm is not only a proxy for past inflation. One
would expect that a longer duration of a wage contract is associated with higher wage
increases. This is in fact borne out by the data as shown in column (8) of the table
although the effect is rather small.
If we add the expected level of unemployment instead of the change in unemployment
as a measure of real activity (column (9)) this slightly increases the coefficients on refer-
ence norms while the coefficient of the level of unemployment itself is insignificant. It is
interesting to note, however, that if we include the expected and the lagged level of unem-
ployment together (column (10)) then these two coefficients are of approximately equal
size but have different signs (as confirmed by a F-test). This implies that the expected
change in unemployment is in fact the more appropriate specification as is suggested by
our theoretical model that implies a wage curve.
We have also conducted a number of other robustness checks that are not shown
in Table 8. In these further specifications we have included, e.g., monthly dummies,
additional lagged variables, sectoral unemployment rates. Furthermore we have also con-
ducted a number of estimations where we have instrumented the explanatory variables of
the benchmark equation in order to account for possible endogeneity. The main results
have again been unaffected by these changes. Finally, we have also run the benchmark
regression specification while assuming that other sectors are the wage leaders. This led
to unconvincing results.
The basic message of the robustness tests in Table 8 is that the main results of the
benchmark specifications are unchanged: reference norms have a considerable impact on
collective wage agreements and their weight seems to be at least as high as the one of
expected inflation. This holds for a large number of samples, different specifications and
in the presence of various additional variables. Furthermore, as shown at the bottom
of Table 8, the condition that β1 + β3 = 1 is only rejected for one of the alternative
specification (column (10)) at the 5% level and for none at the 1% level.
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4 Conclusions
In this paper we have studied the influence of reference norms in an otherwise standard
Taylor model with staggered wages. We have shown that the inclusion of reference norms
considerably increases inflation persistence. On the other hand, we have also shown that
the impact on persistence very much depends on the precise definition of reference norms
and on possible asymmetries in their importance between sectors. In the empirical section
we have documented that reference norms play an important and significant role in the
setting of collectively bargained wages in Austria. The impact of our most preferred mea-
sures of reference norms is typically larger than the impact of expected inflation and in
our benchmark specification its weight is about 60%. The theorectical model of section 2
suggests that a weight of this magnitude is sufficient to produce a reasonable degree of in-
flation persistence. Comparable weights of backward indexation in standard price-setting
models look much more implausible and at odds with the existing survey evidence. When
we compare different concepts of reference norms we find that the leadership norm gives
the best description of the data and that it leads to superior results than the assumption
of external, habit or price indexation norms. These results are confirmed by tests that
use theory-based restrictions on the average parameter estimates, by explicit nested and
non-nested statistical tests and also by an analysis of the temporal pattern of the individ-
ual estimated coefficients. All specifications support the hypothesis that wage leadership
by the metal sector plays a crucial role for wage-setting in Austria.
Taken together, the theoretical and empirical results suggest that differences in ref-
erence norms or the existence of wage leadership can be at least partly responsible for
the observed cross-country differences in inflation persistence and in wage rigidity (cf.
Cecchetti and Debelle, 2006; Dickens et al., 2007; Holden and Wulfsberg, 2007). Differ-
ent reference norms and/or intersectoral differences in the importance of norms can be
reflected in the dispersion of the aggregate measures of persistence across countries. In
this context it is, e.g., interesting to note that the results in Cecchetti and Debelle (2006,
Table 2) indicate that Austria is one of the countries with the lowest degree of inflation
persistence (rank 17 among 19 industrialized countries). This could at least partly reflect
the influence of wage leadership.22 By the same token, our results also offer an explanation
22It would be interesting to study the role of reference norms also for other countries. In order toconstruct a similar dataset as the one used in this paper one would either have to use (official) dataon collectively bargained wages (as for Austria) or directly resort to wage registers maintained by wagesetters (unions or employer federations). This should be possible for a number of European countries(e.g. Germany or the Scandinavian countries).
34ECBWorking Paper Series No 1047April 2009
for the often weak correlation between various measures of wage-setting institutions and
the observed degrees of wage rigidity. A recent summary paper concludes, e.g., that “the
connection between unions and wage rigidity, although it may seem obvious in theory,
appears somewhat shakier in our data than one might expect” (Dickens et al., 2007, p.
211). The results of our paper imply that the shaky and often nor very robust findings
concerning the relation between inflation persistence or real wage rigidity and labor mar-
ket institutions are probably caused by the fact that these institutional variables do not
include measures for the importance, the prevalent type and for possible asymmetries of
reference norms.
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Appendices
A The microfounded model
A.1 Production
The set-up of the model follows Ascari (2000, 2003) and we only want to sketch it here
rather briefly. There is a continuum of industries i ∈ [0, 1] and two sectors (A and B) of
equal size, where sector A consists of the industries in i ∈ [0, 12] and sector B of those in
i ∈ [12, 1]. The wages in both sectors are set by unions where we assume that there is one
union that is attached to each firm. Furthermore, we assume that workers are attached
to their sector and there is no labor mobility between sectors.23 Wages are fixed for two
periods and sector A unions set their wages in periods t = 0, 2, 4, ... while unions in sector
B decide in periods t = 1, 3, 5,....
There is a homogeneous output good Yt that is produced by competitive firms with
the following CES production function:
Yt =
(∫ 1
0
Yθ−1
θit di
) θθ−1
, (16)
where the Yit are intermediate inputs that are necessary to produce the final output and
θ > 1 is the elasticity of substitution between these different intermediate goods. This
leads to the demand functions for intermediate goods:
Yit =
(Pit
Pt
)−θ
Yt, (17)
where the aggregate price index is given by:
Pt =
(∫ 1
0
P 1−θit di
) 11−θ
(18)
The intermediate goods Yit are produced by the firms indexed by i ∈ [0, 1]. Firms
23This is a crucial assumption as argued by Ascari (2003): “Only models with some form of labourimmobility could potentially deliver a substantial degree of persistence” (p. 527, original emphasis ).
40ECBWorking Paper Series No 1047April 2009
have access to a production function:
Yit = AtLαit, (19)
where 0 < α ≤ 1 and where Lit is the amount of labor used by firm i in period t. For the
purpose of this paper we set At = 1 and α = 1 (constant returns to scale). The firms are
assumed to be price takers (perfect competition in intermediate goods production). They
thus set prices equal to marginal costs or:
Pit = Wit (20)
where Wit is the wage rate that firm i faces in period t. Put differently, firms will hire
labor until the real wage equals the marginal product of labor which in this case is just
At = 1.
We can insert (17) and (19) into (20) in order to derive an expression for labor demand
Lit in terms of the wage rate Wit.
Lit = W−θit
(P θ
t Yt
), (21)
A wage-setting union uses equation (21) to take into account the effect of an increase in
the wage rate Wit on labor demand Lit. Due to the assumption that unions are atomistic
they neglect any possible effect of their wages on the aggregate variables Pt and Yt.
A.2 Households
The intertemporal utility function is given by:24
Uj0 =∞∑
s=0
βsu(Cjs,Mjs
Ps
, Ljs) (22)
where β is the time discount factor, Cjs is real consumption,Mjs
Psare real money holdings
and Ljs is labor supply by household j in period s. There is a series of budget constraints:
PtCjt + Mjt + Bjt = ξtMjt−1 + (1 + it−1)Bjt−1 + WjtLjt + Tjt + Hjt (23)
24We abstract in the following from uncertainty as in Ascari (2000). As noted there (FN 7) theintroduction of uncertainty would be straightforward.
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The nominal income in period t consists of a predetermined level of wealth, given by the
money balances Mjt−1 and the amount and interest earned on bonds that are carried
over from period t − 1, i.e. (1 + it−1)Bjt−1. Money holdings are subject to a common
multiplicative shock ξt (see Ascari, 2003). In addition households have labor income
WjtLjt and a lump-sum government transfer Tjt. Households might also receive insurance
payments Hjt that occur in the presence of monetary shock.25 The total nominal income
can be used for purchases of consumption PtCjt, money Mjt and bonds Bjt.
Maximization of (22) with respect to Cjt, Mjt and Bjt+s leads to the FOCs:
uC(Cjt,Mjt
Pt
, Ljt) = β(1 + it)Pt
Pt+1
uC(Cjt+1,Mjt+1
Pt+1
, Ljt+1) (24)
uMP
(Cjt,Mjt
Pt
, Ljt) = uC(Cjt,Mjt
Pt
, Ljt)
(it
1 + it
), (25)
where ux(Cjt,Mjt
Pt, Ljt) =
∂u(Cjt,MjtPt
,Ljt)
∂x. Equations (24) and (25) represent the Euler equa-
tion for consumption and the money demand equation. For a more compact expression
we will write in the following: ux(Cjt,Mjt
Pt, Ljt) = ux(t).
Union j sets the wage for two periods, i.e. under the constraint that Wjt = Wjt+1.
The unions take into account that labor demand Ljt by the firm is given by (21) and
that the income of the household WjtLjt also depends on this magnitude. In particular:
Ljt = W−θjt P θ
t Yt, WjtLjt = W 1−θjt P θ
t Yt (and similar for the second period). Maximization of
(22) with respect to Wjt taking these relations into account thus leads to the wage-setting
equation:
Wjt = − θ
θ − 1
uL(t)P θt Yt + βuL(t + 1)P θ
t+1Yt+1
uC(t)P θ
t Yt
Pt+ βuC(t + 1)
P θt+1Yt+1
Pt+1
(26)
This corresponds to equation (15) in Ascari (2000) and to equation (22) in Huang and
Liu (2002) in a multiperiod framework. In the absence of staggering (26) reduces to the
usual optimality condition:Wjt
Pt= − θ
θ−1uL(t)uC(t)
.
25On this see Ascari (2000, 670) and Huang and Liu (2002).
42ECBWorking Paper Series No 1047April 2009
A.3 Linearizations
We can linearize the FOCs of this model around a zero inflation steady state. The
linearized wage-setting equation can be written as:
wjt = bpt + (1− b)pt+1 + γ(byt + (1− b)yt+1), (27)
where lower case letters stand for deviations around the steady state. Furthermore, b =1
1+βand γ = −ηcc+ηll
1+θηllwhere ηxx ≡ uxxx
uxis the elasticity of the marginal utility of x with
respect to x. In particular, ηcc and ηll are the inverses of the intertemporal elasticity of
substitution of consumption and of labor supply, respectively. Note that for the general
case with decreasing returns to scale (α ≤ 1) we would get: γ =−ηcc+
1θ(1−α)+α
ηll
1+ θθ(1−α)+α
ηll.26 The
wage wjt stands for the wage that is set in period t by union j. Since all unions in a
sector are assumed to be identical we can write wjt = wAt and wjt = wB
t if union j belongs
to sector A (B). Adding the expectation operator and allowing for a sector specific γi
equation (27) corresponds to (2) in the main text.
The price index (18) for the two-sector model is given by
Pt = Wt =
(1
2
(WA
t
)1−θ+
1
2
(WB
t
)1−θ) 1
1−θ
Linearizing this around the steady state leads to:
pt =1
2
(wA
t + wBt
)(28)
This corresponds to equations (4) in the paper.
Finally we can also linearize the FOC conditions (24) and (25). It can be shown that
under specific assumption concerning the multiplicative shock on money holdings ξt the
velocity of money is constant over time. In this case the linearization of (25) leads to:27
−ηccyt = mt − pt (29)
In the paper we focus on the case where ηcc = −1 (which corresponds to a utility function
that is logarithmic in consumption). This is stated in equation (5).
26See Ascari (2000, p. 674) and Ascari (2003, 520f.).27See Ascari (2003, p. 514f.) and Ascari (2000, FN 23).
43ECB
Working Paper Series No 1047April 2009
B The derivation of λi
We can insert (4), (5) and (6) into (1) to derive:
wit = ψi
1w−it−1 + ψi
2Etw−it+1 + ψi
3mt (30)
where ψi1 = b(1−γi)(1−μi)+2μi
1+μi+γi(1−μi), ψi
2 = (1−b)(1−γi)(1−μi)1+μi+γi(1−μi)
, ψi3 =
2γi(1−μi)(b+ρ(1−b))
1+μi+γi(1−μi). Note that for
t = 0, 2, 4, ... it holds that i = A and (−i) = B, while for t = 1, 3, 5, ... we have that i = B
and (−i) = A. There exists various ways to solve this forward-looking difference equation.
We choose the method of undetermined coefficients and start with the conjecture that
the solution for wAt is of the form:
wAt = λAwB
t−1 + θAmt (31)
The parallel conjecture for wBt+1 is that:
wBt+1 = λBwA
t + θBmt+1 (32)
From (32) together with (6) it follows that EtwBt+1 = λBwA
t + θBρmt. We can insert this
expression into (30) to derive that:
wAt =
ψA1
1− ψA2 λB
wBt−1 +
ψA2 θBρ + ψA
3
1− ψA2 λB
mt (33)
In an analogous way we can derive that:
wBt+1 =
ψB1
1− ψB2 λA
wAt +
ψB2 θAρ + ψB
3
1− ψB2 λA
mt+1 (34)
Comparing (31) with (33) and (32) with (34) we see that the equilibrium values for
λA, λB, θA and θB are implicitly given as the solutions to the following system of four
equations: λA =ψA
1
1−ψA2 λB , λB =
ψB1
1−ψB2 λA , θA =
ψA2 θBρ+ψA
3
1−ψA2 λB and θB =
ψB2 θAρ+ψB
3
1−ψB2 λA . For the
crucial parameter λi the solutions come out as:
λA =2ψA
1
1− ψA2 ψB
1 + ψA1 ψB
2 +
√(1 + ψA
2 ψB1 − ψA
1 ψB2 )
2 − 4ψA2 ψB
1
(35)
44ECBWorking Paper Series No 1047April 2009
λB =1 + ψA
2 ψB1 − ψA
1 ψB2 −
√(1 + ψA
2 ψB1 − ψA
1 ψB2 )
2 − 4ψA2 ψB
1
2ψA2
(36)
For the symmetric case with μA = μB = μ and γA = γB = γ (and in addition with b = 12)
we can derive that:
λA = λB = λ =1−√1− 4ψ1ψ2
2ψ2
where ψ1 = 12
(1−γ)(1−μ)+2μ1+μ+γ(1−μ)
and ψ2 = 12
(1−γ)(1−μ)1+μ+γ(1−μ)
. Inserting these values for ψ1 and ψ2
gives (9) in the main text. We can take this expression to calculate:
∂λ∂γ
= −1+μ2+γ(1−μ2)−2√
γ(1−μ2)+μ2
(1−γ)2(1−μ)√
γ(1−μ2)+μ2< 0
∂λ∂μ
= −2(γ(1−μ)+μ−
√γ(1−μ2)+μ2
)
(1−γ)(1−μ)2√
γ(1−μ2)+μ2> 0
Note that from (31) and (32) we can derive that:
wAt = λAwB
t−1 + θAmt = ΛwAt−2 + θAmt + λAθBmt−1
wBt+1 = λBwA
t + θBmt+1 = ΛwBt−1 + θBmt+1 + λBθAmt,
where we have defined that Λ ≡ λAλB. This measure for annual persistence is the same
in both sectors even if μA �= μB and γA �= γB. For this reason we use it frequently as our
preferred measure of persistence in the main text.
45ECB
Working Paper Series No 1047April 2009
C The data
C.1 Sectoral wage change data
C.1.1 The basic index series
Our collective bargaining wage data are based on detailed series of the Tariflohnindex
(TLI, “Index of Agreed Minimum Wages”), a monthly database maintained by Statistics
Austria. The TLI is a Laspeyres index of sectoral collectively negotiated minimum wages
according to a particular base year. Predominantly, our data are from the TLI 1986 (for
the years 1986 - 2006). For 1979 - 1985 we use the TLI 1976. Individual series are chained
with the ratio of the annual average TLI 1986 to the TLI 1976 in 1986.28 Wage changes in
a particular year are the relative changes of the TLI index compared to the last change. In
total, we thus have 27 years of collective wage changes. As the system of wage leadership
is only in place since the beginning of the 1980s (cf. Traxler et al., 2008) we do not use
data from previous years.
Typically, these indices are analyzed only at rather high levels of aggregation. However,
Statistics Austria also published more detailed monthly index values which are - at the
most disaggregate level - identical, or come close to, individual collective agreements.
There are 125 such indices in the TLI 1986 which are mostly for branches and separately
for blue-collar and white-collar workers. While most of these refer to collective agreements
for the whole country, some of these series cover only one federal state (Bundesland).
Sometimes, there is also a distinction between “industry” and “trade” (Gewerbe). All of
this reflects the practice of collective bargaining in Austria. Some examples are “blue-
collar workers in the paper-processing trades”, “blue-collar workers in the metal industry”,
“white-collar workers in the clothing and textile industry in Vorarlberg”, and “white-collar
workers in insurance companies”.
Furthermore, there are several indices for the public sector (e.g. for workers in the
federal administration) and a few series for (mainly) publicly owned transport companies
(such as the Osterreichische Bundesbahnen). A full list of all 125 TLI series is given in
Table C-1 which is structured along the partiton of collective agreements in blue-collar,
white-collar and public sector workers as well as workers in public transport. Within each
28For detailed information we refer to Statistics Austria publications such as Tariflohnindex 1986.Aufbau und Gewichtung (Vienna, 1988) and Tariflohnindex 1976. Aufbau und Gewichtung (Vienna, 1978).Basic information can also be found in Statistics Austria’s monthly publication Statistische Nachrichtenin no. 6/1978 and no. 1/1988. We thank Markus Bonisch and Helga Maurer for delivering these dataand giving us background information.
46ECBWorking Paper Series No 1047April 2009
partition, the series names are listed in decending order of the TLI 1986 weight.
Table C-1: List of all 125 basic TLI 1986 units
Altogether, these 125 basic series of the Tariflohnindex - or as we call them - “TLI
47ECB
Working Paper Series No 1047April 2009
units” or simply “units” represent 194 collective agreements.29 Mostly, a TLI index re-
presents only one collective agreement. However, there are cases when such an index
covers two ore more agreements. The most notable examples are the series for blue-collar
workers in the food industry which aggregates 10 agreements, the series for white-collar
workers in wholesale and retail trade representing 10 agreements and the series for blue-
collar workers in “supplementary construction trades” (Bauhilfsgewerbe) standing for 9
agreements.
C.1.2 Data checks and “quality” of the TLI series
Previous knowledge and the observation of collective bargaining in Austria suggest that
most collective agreements last for exactly one year. The question was whether such a
regular pattern could also be observed in the data.
Each of the 125 TLI series was scrutinized in which months there was a change in
the index and by how much it changed. All series are monotonically increasing in time
(collective wages are nominally rigid downwards). Besides that, there was a substantial
amount of irregularities. For example, the month of the wage change was not constant. It
shifted especially in the 1970s where - apparently - the time structure of wage negotiations
shifted markedly (putting the system of wage leadership into place). Moreover, in quite a
lot of units there was more than one change of the index in one year whereas in other series
or years there was no change at all (most notably in the public sector where there was
a “wage freeze” in 1996 and 1997). In such cases we tried to distinguish with great care
between “main” and “minor” changes in the index. (Some of these minor changes were
easily explained by rounding differences due to chaining the TLI 1986 with the TLI1976,
to the introduction of the Euro or to changes in data processing.) In most cases, it was
quite obvious to determine the month of the wage change. With this information we
computed the associated wage change between those months (where it was possible that
there was no wage change at all in a particular year).
There were, however, also units where the judgement was difficult, e.g. where there
were many index changes spread over the year. Based on the overall impression of how
regularly (i.e. not too often or not too rarely) the index figures increased we subjectively
29There are considerably more such agreements, however our data comprise all major collective agree-ments and the data are constructed to give a representative picture of all collective agreements. Accordingto the Austrian Federation of Trade Unions (OGB), in a typical year, there are more than 400 collec-tive agreements (without supplemental agreements at the firm level which do not cover wages). Source:Jahresbericht des OGB 2005.
48ECBWorking Paper Series No 1047April 2009
classified TLI units into three “qualities”: 86 units were assigned to quality 1 (the best
category), 14 to quality 2 and 25 to quality 3. In our estimations we only used those 100
series with quality 1 or 2. See Table C-1 for the “quality” assigned to all units.
The more agreements are subsumed by an individual TLI series, the more likely it is
that we cannot use it in our analysis because wage negotiations may take place in different
months and we cannot identify the variables that we are interested in, i.e. the month of
the wage change, the associated wage change and the contract length. A typical example
is the index for blue-collar workers in the food industry which increases several times a
year and was thus classified as “quality 3”. The same is true for white-collar workers in
the same industry.30 Smaller units which we considered not to use include “blue-collar
workers in other trades” (the name indicates that it is a composite of different branches),
“blue-collar workers in the clothing industry” where there are several wage changes in
almost every year and the associated months show no regular pattern. Finally, we also
classified the index series of workers employed by professionals (such as doctors, lawyers
and chemists) as “quality 3” because these are not included in the TLI 1976.
C.1.3 Panel structure of the data
If we use only index series with quality 1 or 2 we would have 2700 (100*27) wage change
observations if there were exactly one wage change per year. However, the panel is not
completely balanced. 27 annual wage change observations are available only for 49 units.
In all other series at most 3 observations are missing. One reason for such gaps is that
sometimes an agreement lasts longer than a year which could mean that no wage change
is observable in a particular year (the most important example being the aforementioned
three-year public-sector wage freeze in the 1990s which affected 19 series). We end up
with 2621 wage change observations for 100 units in 27 years.
C.1.4 “Independent” TLI units
Although wage negotiations in many sectors are conducted separately for blue- and white-
collar workers they are very often synchronous and the wage changes are very similar. The
same holds for collective agreements of similar or related sectors. One could suspect wage
negotiations in such cases are in effect strongly interwoven (as casual observations of
30On the other hand, the indices for the white-collar workers in wholesale or retail trade and the one forblue-collar workers in “supplementary construction trades” are usable because apparently the underlyingcollective agreements are synchronous.
49ECB
Working Paper Series No 1047April 2009
current wage settlements also suggests). The same also holds for wages in the public
sector.
As a robustness check, based on a subjective assessment of whether there is a high
correlation and near-synchrony of wage changes (paired with an obvious relatedness be-
tween units), we grouped a number of series together and let each of these groups be
represented by one of them (mostly the largest unit). For example, in construction four
series were merged (construction industry and construction trade, both for blue-collar and
white-collar workers). Note especially that four series of the metal and mining industries
(again, for both blue-collar and white-collar workers) were grouped together. These con-
stitute the group of wage-leading units (see below). Most importantly, 18 index series
belonging to the public sector were also treated as one unit in this exercise. Altogether,
these aggregations reduced the number units from 100 to 55. Our estimation results were
hardly affected by this, as column (5) in Table 8 suggests.
C.2 Other data
C.2.1 Macro forecast data
We assume that expectations over inflation and real activity are shaped by forecast data
of the Austrian Institute of Economic Research (WIFO). The WIFO is Austria’s oldest
economic research institute and its forecasts are said to be especially relevant for wage
setting. This is plausible, because it is (partly) owned by the social partners and has close
ties to them. We use series for real GDP growth, inflation (measured by the consumer price
index) and the unemployment rate (based on registered employment and unemployment
data).31
The WIFO projections have for a long time been published regularly at the end of each
quarter. Typically, forecasts are made for the current as well as for the next year. However,
until 1980, next-year forecasts were only provided with the September and December
projections. Between 1981 and 1988, next-year forecasts were also published in June, and
since 1989 each of the four annual projections (i.e. also the one in March) include both
current- and next-year forecasts. In June 1997 there was no WIFO projection.
Our estimation equation (15) for each wage change is based on the most recent forecast
available in each month of every year to construct a forecast exactly one year ahead.
However, this would not be possible for many months in the period between 1980 to 1988
31We thank Josef Baumgartner for providing us with the forecast series.
50ECBWorking Paper Series No 1047April 2009
because next-year forecasts are missing. So we had to make some assumptions how to
fill in these “missing” forecast values. All forecasts for June 1997 were imputed as the
simple averages of March and September 1997. To get the needed next-year forecasts for
the years between 1980 and 1988 we experimented with two different approaches: In the
first one we assumed that the forecast for the next year is equal to the forecast for the
current year. In the second approach the assumption was that the next-year forecast of a
variable is a weighted average of this year’s forecast for that variable and that of the next
year in September (where we have next-year forecasts throughout all observations). The
weights are 0.75 for the current year and and 0.25 for next year for projections in March
and 0.5 for the current year and 0.5 for the next year for projections in June, respectively.
In the empirical exercises we sticked to the second approach but did not find substantial
differences between both imputation approaches.
Table C-2: Imputations of WIFO macroeconomic forecasts
C.2.2 Month-specific growth rates, forecasts and forecast errors
As different sectors reach agreements in different months of a particular year it is im-
portant to construct month-specific macroeconomic variables. As far as past values are
51ECB
Working Paper Series No 1047April 2009
concerned the change of a macro variable x in a particular month over the last year is
computed by weighted annual averages: Δxj,τ = j−112
Δxτ + 12−j+112
Δxτ−1 where j and τ
are subscripts for month and year, respectively. For example, the inflation rate over the
last 12 months in May 2003 is given by Δp5,2003 = 412
Δp2003 + 812
Δp2002. Equivalently, we
deal with GDP growth and changes of the unemployment rate.
As far as forecasts are concerned we have to be careful to represent as exactly as
possible the expectations wage setters had at that time. We use a similar procedure as
for the past values. In this case we define by Δxfcj,τ the expected change of x over the
upcoming year starting in month j of year τ . Again, we use weighted yearly averages.
This means that Δxfcj,τ = 12−j+1
12Δxfc
τ + j−112
Δxfcτ+1 where Δxfc
τ and Δxfcτ+1 are given by
the WIFO projections for Δx for the years τ and τ + 1, respectively. As there are four
projections in each year (see above) we had to decide which of them is relevant in a
particular month j. We proceeded as follows:
Table C-3: Allocation of WIFO projections to
months of wage changes
Month of wage change Relevant WIFO projection
1, 2, 3 December (last year)
4, 5, 6 March (current year)
7, 8, 9 June (current year)
10, 11, 12 September (current year)
In months 2 and 3 of a year τ there is a further difficulty, namely how to get a forecast
for a full year ahead because the only macroeconomic projection available is the one
from December in the previous year containing only forecasts for τ − 1 and τ . However
one would also need a forecast for τ + 1 which is only available with the next (March)
projection. In such a case we simply set the forecast for τ + 1 equal to that for τ .
One could object it is implausible that for a wage settlement that becomes effective,
say, in April the relevant projection is from the end of March. However, in most cases,
not very much time passes between the point in time a settlement is reached and when it
becomes effective (this time span is usually less than a month). It is also likely that wage
setters are influenced by “rumours” about the outcome of the pending WIFO macroeco-
nomic projection.
52ECBWorking Paper Series No 1047April 2009
We use these constructed values Δxfcj,τ as proxies for the month-specific expectations
of inflation (Ej,τΔpj,τ ) and real activity (Ej,τΔyj,τ ) in equation (15). Finally, after hav-
ing constructed one-year-ahead forecasts and past-year-changes for the relevant macro
variables in each month forecast errors are defined as Δxerrj,τ = Δxj,τ −Δxfc
j,τ−1.
C.3 Construction of reference norms
C.3.1 External reference norm
Call D(i, j, τ) the date when unit i sets its new wage in month j in year τ . The external
reference norm is assumed to be given by the (weighted) average wage increase of all
other (i.e. excluding i) units that have set new wages since D(i, j′, τ ′), that is, since the
last time the unit i has set its wage. Normally, j′ is identical or close to j and, usually,
τ ′ = τ − 1 but, as explained, the time distance could be up to three years.
C.3.2 Wage leadership norm
This is simply the wage increase of the blue-collar workers32 in the metal industry whereas
for the wage-leading units themselves (blue-collar/white-collar workers in the metal and
the mining industry, respectively) this norm is set to zero. If wage negotations for a TLI
unit take place in November or December then we use the metal-sector wage change of
the current year, in all other months (January to October) last-year wage changes.
32There are two series for the metal industry as the TLI also contains the one for white-collar workers.Wage increases are most often, but not always identical. Given the higher union density and power ofthe metal workers’ union (which represents the blue-collar workers of that industry whereas white-collarworkers are organized in another union) we chose the series of blue-collar workers as the wage leader.
53ECB
Working Paper Series No 1047April 2009
Figures and Tables
Figure 1 – The Effect of the Importance of Reference Norms on Inflation Persistence
0.0
0.2
0.4
0.6
0.8
1.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
μ
=0.2 =0.3
Note: The figure reports the degree of annual inflation persistence as the importance of reference norms increases from 0BA to 1 for =0.2 and =0.3.
54ECBWorking Paper Series No 1047April 2009
Table 1 – The Effect of Different Reference Norms on Inflation Persistence
μ =0 μ =0.25 μ =0.5
A. External Norms
=0.2 0.146 0.444 0.702 =0.3 0.085 0.332 0.602
B. Price Indexation Norms
=0.2 0.146 0.314 0.539 =0.3 0.085 0.216 0.425
C. Habit-Persistence Norms
=0.2 0.146 0.721 0.916 =0.3 0.085 0.648 0.884
Note: The numbers report the degree of annual persistence BA for three alternative reference norms (explained in the text) and various degrees of real rigidity ( ) and the importance of reference norms (μ). For the habit persistence norm the measure of persistence is the sum of the first two autoregressive terms.
Table 2 – The Effect of Asymmetries in Reference Norms on Inflation Persistence
No
Reference Norms ( 0 )
Symmetric Reference Norms
( 5.0 )
Asymmetric Reference Norms
( 5.0 ) 0BA 5.0BA 1,0 BA =0.2 0.146 0.702 0.5 =0.3 0.085 0.602 0.368
Note: The numbers report the degree of annual persistence BA when wage-setters have external reference norms as explained in the text.
55ECB
Working Paper Series No 1047April 2009
Tabl
e 3
– Su
mm
ary
Stat
istic
s on
Indi
vidu
al C
olle
ctiv
e W
age
Agr
eem
ents
in A
ustr
ia, 1
980-
2006
Gro
wth
Rat
e of
Wag
es
Qua
rter
of N
ew W
age
Agr
eem
ents
Le
ngth
of N
ew A
gree
men
ts (i
n m
onth
s)
Yea
r M
ean
Std.
Dev
. W
inte
r Sp
ring
Su
mm
er
Fall
No
Con
trac
t12
<1
2
13-2
4
>24
19
80
0.05
96
0.02
07
44%
24
%
13%
17
%
2%
76%
3%
19
%
2%
1981
0.
0767
0.
0209
45
%
24%
12
%
16%
3%
87
%
1%
9%
3%
1982
0.
0647
0.
0114
47
%
24%
11
%
16%
2%
58
%
4%
36%
2%
19
83
0.04
63
0.00
98
43%
28
%
12%
16
%
1%
60%
26
%
13%
1%
19
84
0.04
45
0.00
95
43%
30
%
9%
16%
2%
89
%
1%
8%
2%
1985
0.
0530
0.
0059
46
%
29%
8%
17
%
0%
89%
1%
10
%
0%
1986
0.
0449
0.
0111
47
%
28%
8%
13
%
4%
87%
2%
7%
4%
19
87
0.03
06
0.00
52
48%
30
%
8%
13%
1%
65
%
2%
32%
1%
19
88
0.02
81
0.00
96
24%
31
%
32%
12
%
1%
64%
26
%
9%
1%
1989
0.
0377
0.
0146
49
%
30%
6%
14
%
1%
95%
0%
4%
1%
19
90
0.06
20
0.01
60
48%
31
%
7%
14%
0%
93
%
3%
4%
0%
1991
0.
0665
0.
0095
49
%
31%
7%
13
%
0%
98%
1%
1%
0%
19
92
0.05
36
0.00
89
49%
31
%
7%
13%
0%
94
%
0%
6%
0%
1993
0.
0440
0.
0166
49
%
26%
7%
17
%
1%
90%
6%
3%
1%
19
94
0.03
24
0.00
78
51%
28
%
7%
13%
1%
92
%
2%
5%
1%
1995
0.
0329
0.
0081
49
%
30%
6%
12
%
3%
66%
4%
7%
23
%
1996
0.
0200
0.
0127
33
%
28%
4%
14
%
21%
62
%
2%
14%
22
%
1997
0.
0178
0.
0122
26
%
30%
6%
14
%
24%
62
%
5%
9%
24%
19
98
0.02
25
0.00
66
47%
31
%
7%
15%
0%
85
%
6%
9%
0%
1999
0.
0238
0.
0067
47
%
30%
4%
19
%
0%
94%
3%
3%
0%
20
00
0.01
98
0.00
71
48%
28
%
4%
17%
3%
93
%
2%
2%
3%
2001
0.
0298
0.
0356
50
%
29%
4%
16
%
1%
90%
2%
7%
1%
20
02
0.02
17
0.00
82
49%
31
%
4%
13%
3%
91
%
2%
4%
3%
2003
0.
0220
0.
0064
50
%
33%
4%
11
%
2%
94%
0%
4%
2%
20
04
0.01
99
0.00
55
52%
32
%
5%
9%
2%
93%
1%
4%
2%
20
05
0.02
44
0.00
51
51%
33
%
6%
10%
0%
94
%
3%
2%
1%
2006
0.
0250
0.
0045
53
%
32%
5%
9%
1%
–
– –
– To
tal
0.03
79
0.02
12
46%
29
%
9%
13%
3%
80
%
4%
9%
7%
Note
: The
num
bers
in th
e ta
ble
refe
r to
the
sam
ple
of 1
00 w
age-
setti
ng u
nits
com
prisi
ng 9
2% o
f the
tota
l lab
or fo
rce.
The
num
bers
are
unw
eigh
ted.
The
qua
rters
are
def
ined
as
follo
ws:
Win
ter (
Jan.
, Feb
., M
ar.),
Spr
ing
(Apr
., M
ay, J
un.),
Sum
mer
(Jul
., A
ug.,
Sep.
), Fa
ll (O
ct.,
Nov
., D
ec.).
The
leng
th o
f new
agr
eem
ents
refe
rs to
the
year
whe
n th
ey st
art.
56ECBWorking Paper Series No 1047April 2009
Tabl
e 4a
– D
eter
min
ants
of C
olle
ctiv
e W
age
Agr
eem
ents
(Ext
erna
l Ref
eren
ce N
orm
s)
Dep
ende
nt V
aria
ble:
gro
wth
rate
of u
nit-s
peci
fic w
age
rate
s (i j
w,
)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Estim
atio
n M
etho
d FE
R
E R
C
MG
FE
R
E R
C
MG
Ex
tern
al N
orm
0.
551*
**
0.54
8***
0.
571*
**
0.55
1***
0.
636*
**
0.63
5***
0.
655*
**
0.65
0***
(0.0
25)
(0.0
26)
(0.0
39)
(0.0
34)
(0.0
24)
(0.0
24)
(0.0
35)
(0.0
30)
Infla
tion
(fore
cast
) 0.
595*
**
0.59
0***
0.
550*
**
0.58
8***
0.
578*
**
0.57
3***
0.
545*
**
0.57
8***
(0.0
34)
(0.0
34)
(0.0
41)
(0.0
35)
(0.0
32)
(0.0
31)
(0.0
42)
(0.0
37)
GD
P gr
owth
(for
ecas
t) 0.
328*
**
0.32
6***
0.
327*
**
0.32
8***
–
– –
–
(0.0
36)
(0.0
35)
(0.0
46)
(0.0
42)
Cha
nge
in u
nem
ploy
men
t rat
e
– –
– –
-1.2
26**
* -1
.240
***
-1.1
50**
* -1
.212
***
(for
ecas
t)
(0
.094
) (0
.093
) (0
.11)
(0
.099
) Ti
me
(Dec
ade)
Dum
mie
s Y
ES
YES
Y
ES
YES
Y
ES
YES
Y
ES
YES
C
onst
ant
-0.0
0801
***
-0.0
0767
***
-0.0
0741
***
-0.0
078*
**
-0.0
0144
* -0
.001
19
-0.0
0154
* -0
.002
1***
(0.0
010)
(0
.001
1)
(0.0
012)
(0
.001
) (0
.000
81)
(0.0
0086
) (0
.000
92)
(0.0
0068
) O
bser
vatio
ns
2621
26
21
2621
26
21
2621
26
21
2621
26
21
Num
ber o
f gro
ups
100
100
100
100
100
100
100
100
Test
-sta
tistic
for R
ando
m E
ffect
s –
83.0
4 –
– –
78.3
8 –
–-
Prob
abili
ty v
alue
0.00
0
0.00
0
2 -s
tatis
tic fo
r H0:
Para
met
er
Con
stan
cy
– –
1664
.14
–
– –
1623
.08
–
Prob
abili
ty v
alue
of H
0 –
– 0.
000
– –
– 0.
000
– Su
m:
norm
infl
ˆˆ
1.
146
1.13
8 1.
121
1.13
9 1.
214
1.20
8 1.
2 1.
228
F-st
atis
tic fo
r H0:
1ˆ
ˆno
rmin
fl
49.5
06
41.3
8 28
.296
8.
089
94.8
34
87.0
7 68
.31
23.1
72
Prob
abili
ty v
alue
of H
0 0.
000
0.00
0 0.
000
0.00
5 0.
000
0.00
0 0.
000
0.00
0 No
te: T
he ta
bles
con
tain
the
resu
lt of
pan
el e
stim
atio
ns o
f the
det
erm
inan
ts o
f uni
t-spe
cific
col
lect
ive
wag
e ag
reem
ents
i j
w,
in A
ustri
a, w
here
i=1,
2, …
, 100
, j=1
, 2, …
, 12
and
t=19
80, 1
981,
…, 2
006.
The
esti
mat
ion
uses
the
assu
mpt
ion
of e
xter
nal r
efer
ence
nor
ms
and
GD
P gr
owth
(co
lum
ns (
1) to
(4)
) or
the
chan
ge in
the
unem
ploy
men
t rat
e (c
olum
ns (5
) to
(8))
as a
mea
sure
of r
eal a
ctiv
ity. T
he ti
me
dum
mie
s are
def
ined
as d
ecad
e du
mm
ies (
i.e. f
or 1
980-
1989
, 199
0-19
99, e
tc.).
For
eac
h m
odel
we
repo
rt th
e re
sults
of
a fix
ed e
ffec
ts (F
E), a
ran
dom
eff
ects
(R
E), a
ran
dom
coe
ffic
ient
s (R
C)
and
a m
ean
grou
p (M
G)
estim
atio
n. I
n co
lum
ns (
2) a
nd (
6) w
e re
port
the
Han
sen-
Sarg
an s
tatis
tic f
or
over
iden
tifyi
ng re
stric
tions
in o
rder
to te
st fo
r the
app
ropr
iate
ness
of t
he R
E sp
ecifi
catio
n. F
or th
e R
C e
stim
atio
n w
e re
port
the
2 sta
tistic
s fo
r par
amet
er c
onst
ancy
pro
pose
d by
Sw
amy
(197
0). F
or a
ll sp
ecifi
catio
ns w
e al
so g
ive
the
sum
of t
he c
oeffi
cien
ts o
n th
e no
rm a
nd th
e in
flatio
n fo
reca
sts a
nd a
lso
the
F-st
atis
tic a
nd th
e p-
valu
e of
test
ing
whe
ther
this
su
m is
equ
al to
1. S
tand
ard
erro
rs a
re in
par
enth
eses
. ***
, **
and
* de
note
stat
istic
al si
gnifi
canc
e at
the
1, 5
and
10
% le
vel,
resp
ectiv
ely .
57ECB
Working Paper Series No 1047April 2009
Tabl
e 4b
– D
eter
min
ants
of C
olle
ctiv
e W
age
Agr
eem
ents
(Wag
e Le
ader
ship
Ref
eren
ce N
orm
s)
Dep
ende
nt V
aria
ble:
gro
wth
rate
of u
nit-s
peci
fic w
age
rate
s (i j
w,
)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Estim
atio
n M
etho
d FE
R
E R
C
MG
FE
R
E R
C
MG
Le
ader
ship
Nor
m
0.56
6***
0.
346*
**
0.57
8***
0.
599*
**
0.56
1***
0.
348*
**
0.57
9***
0.
594*
**
(0
.018
) (0
.027
) (0
.025
) (0
.021
) (0
.017
) (0
.026
) (0
.026
) (0
.022
) In
flatio
n (f
orec
ast)
0.
496*
**
0.71
5***
0.
439*
**
0.43
6***
0.
519*
**
0.73
9***
0.
454*
**
0.46
6***
(0.0
26)
(0.0
37)
(0.0
31)
(0.0
25)
(0.0
27)
(0.0
37)
(0.0
34)
(0.0
28)
GD
P gr
owth
(for
ecas
t) 0.
0919
***
0.18
7***
0.
0751
* 0.
0568
–
– –
–
(0.0
32)
(0.0
36)
(0.0
42)
(0.0
38)
Cha
nge
in u
nem
ploy
men
t rat
e
– –
– –
-0.3
65**
* -0
.591
***
-0.2
19**
-0
.260
***
(for
ecas
t)
(0
.086
) (0
.094
) (0
.10)
(0
.088
) Ti
me
(Dec
ade)
Dum
mie
s Y
ES
YES
Y
ES
YES
Y
ES
YES
Y
ES
YES
C
onst
ant
-0.0
0270
***
-0.0
0134
-0
.002
23**
-0
.002
4***
-0
.000
428
0.00
306*
**
-0.0
0074
9 -0
.002
4***
(0.0
0093
) (0
.001
00)
(0.0
011)
(0
.000
86)
(0.0
0071
) (0
.000
86)
(0.0
0093
) (0
.000
69)
Obs
erva
tions
26
21
2621
26
21
2621
26
21
2621
26
21
2621
N
umbe
r of g
roup
s 10
0 10
0 10
0 10
0 10
0 10
0 10
0 10
0 Te
st-s
tatis
tic fo
r Ran
dom
Effe
cts
– 48
5.36
–
– –
461.
91
– –
Prob
abili
ty v
alue
0.00
0
0.00
0
Te
st st
atis
tic fo
r H0:
Para
met
er
Con
stan
cy
– –
3317
.48
– –
– 30
68.6
4 –
Prob
abili
ty v
alue
of H
0 –
– 0.
000
– –
– 0.
000
– Su
m:
norm
infl
ˆˆ
1.
062
1.06
2 1.
017
1.03
5 1.
081
1.08
8 1.
033
1.06
F-st
atis
tic fo
r H0:
1ˆ
ˆno
rmin
fl
10.4
66
8.15
8 0.
595
1.18
8 15
.183
15
.259
1.
866
2.85
3 Pr
obab
ility
val
ue o
f H0
0.00
1 0.
004
0.44
0.
276
0.00
0 0.
000
0.17
2 0.
091
Note
: The
tabl
es c
onta
in th
e re
sult
of p
anel
est
imat
ions
of t
he d
eter
min
ants
of u
nit-s
peci
fic c
olle
ctiv
e w
age
agre
emen
ts
i jw
, in
Aus
tria,
whe
re i=
1, 2
, …, 1
00, j
=1, 2
, …, 1
2 an
d t=
1980
, 198
1, …
, 200
6. T
he e
stim
atio
n us
es th
e as
sum
ptio
n of
lead
ersh
ip re
fere
nce
norm
s an
d G
DP
grow
th (c
olum
ns (1
) to
(4))
or th
e ch
ange
in th
e un
empl
oym
ent r
ate
(col
umns
(5) t
o (8
)) a
s a m
easu
re o
f rea
l act
ivity
. The
tim
e du
mm
ies a
re d
efin
ed a
s dec
ade
dum
mie
s (i.e
. for
198
0-19
89, 1
990-
1999
, etc
.). F
or e
ach
mod
el w
e re
port
the
resu
lts o
f a
fixed
eff
ects
(FE)
, a r
ando
m e
ffec
ts (
RE)
, a r
ando
m c
oeff
icie
nts
(RC
) an
d a
mea
n gr
oup
(MG
) es
timat
ion.
In
colu
mns
(2)
and
(6)
we
repo
rt th
e H
anse
n-Sa
rgan
sta
tistic
for
ov
erid
entif
ying
restr
ictio
ns in
ord
er to
test
for t
he a
ppro
pria
tene
ss o
f the
RE
spec
ifica
tion.
For
the
RC
est
imat
ion
we
repo
rt th
e 2 s
tatis
tics
for p
aram
eter
con
stan
cy p
ropo
sed
by
Swam
y (1
970)
. For
all
spec
ifica
tions
we
also
giv
e th
e su
m o
f the
coe
ffic
ient
s on
the
norm
and
the
infla
tion
fore
cast
s and
als
o th
e F-
stat
istic
and
the
p-va
lue
of te
stin
g w
heth
er th
is
sum
is e
qual
to 1
. Sta
ndar
d er
rors
are
in p
aren
thes
es. *
**, *
* an
d *
deno
te st
atist
ical
sign
ifica
nce
at th
e 1,
5 a
nd 1
0 %
leve
l, re
spec
tivel
y .
58ECBWorking Paper Series No 1047April 2009
Table 5 – Comparison of Different Reference Norms with J-Tests
t-statistic on the fitted values from a regression including
Leadership Norm External Norm Habit Norm Price Indexation Norm
In regression including:
Leadership Norm – 3.592 (0.000)
2.804 (0.000)
0.332 (0.74)
External Norm 6.996* (0.000) – 2.07
(0.038) 0.648
(0.517)
Habit Norm 20.481* (0.000)
15.357* (0.000) – 3.123
(0.002)
Price Indexation Norm 20.955* (0.000)
16.09* (0.000)
10.946* (0.000) –
Note: The values in the table are based on an approach where the fitted value of a benchmark regression with the respective reference norm in the column is added to a regression that includes the reference norm in the respective row. The numbers reported are the t-statistic of these fitted values while p-values are shown in parentheses. A “*” indicates that the t-statistic in one pair of comparisons is higher than in the case where the role of the two reference norms is reversed.
Table 6 – Nested Comparison of Different Reference Norms
Dependent Variable: growth rate of unit-specific wage rates ( itw )
(1) (2) (3) (4) (5) (6) Leadership Norm 0.412*** 0.563*** 0.577*** – – – (0.059) (0.027) (0.028) External Norm 0.279*** – – 0.718*** 0.661*** – (0.078) (0.047) (0.041) Habit Norm – 0.065* – -0.065** – 0.307*** (0.023) (0.032) (0.028) Price Indexation Norm – – -0.016 – -0.037 0.178*** (0.048) (0.056) (0.057) Inflation (forecast) YES YES YES YES YES YES Change in unemployment rate (forecast)
YES YES YES YES YES YES
Time (Decade) Dummies YES YES YES YES YES YES Constant YES YES YES YES YES YES Note: The table contains the results if two reference norms are included in pairs into the benchmark estimation (column (7) of Table 4b).
59ECB
Working Paper Series No 1047April 2009
Table 7 – Rejection Rate for the Individual Coefficients
Significantly different from 1(5% level)
Significantly different from 1(1% level)
Leadership Norm 15% 6%
External Norm 69% 51%
Habit Norm 89% 60%
Price Indexation Norm 27% 11%
No Reference Norm 23% 9%
Note: The table contains the percentage of the 100 wage-setting units for which the condition 1ˆˆinf
inorm
i on their individual coefficients is violated. The results are based on the RC estimation with the change in the unemployment rate as the measure of real activity.
60ECBWorking Paper Series No 1047April 2009
Tab
le 8
– R
obus
tnes
s Tes
ts fo
r th
e B
ench
mar
k E
stim
atio
n (le
ader
ship
ref
eren
ce n
orm
s)
Dep
ende
nt V
aria
ble:
gro
wth
rate
of u
nit-s
peci
fic w
age
rate
s (i tw)
Estim
atio
n M
etho
d R
C
RC
R
C
RC
R
C
RC
R
C
RC
R
C
RC
Ben
chm
ark
<199
3 >=
1993
O
nly
priv
. se
ctor
O
nly
inde
p.un
its.
Fore
cast
Er
rors
C
ontra
ct
Leng
th
Past
In
flatio
n Le
vel o
f U
nr
Leve
l and
La
g of
unr
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
Le
ader
ship
Nor
m
0.57
9***
0.51
7***
0.43
6***
0.60
8***
0.62
5***
0.57
0***
0.58
3***
0.57
7***
0.61
7***
0.62
5***
(0.0
26)
(0.0
24)
(0.0
99)
(0.0
30)
(0.0
35)
(0.0
42)
(0.0
26)
(0.0
28)
(0.0
31)
(0.0
31)
Infla
tion
(for
ecas
t) 0.
454*
**0.
458*
**0.
531*
**0.
437*
**0.
416*
**0.
460*
**0.
449*
**0.
479*
**0.
402*
**0.
482*
**
(0
.034
) (0
.039
) (0
.068
) (0
.039
) (0
.046
) (0
.060
) (0
.034
) (0
.054
) (0
.041
) (0
.045
) C
hang
e in
une
mpl
oym
ent r
ate
(for
ecas
t) -0
.219
**-0
.326
***
-0.1
05
-0.2
30*
-0.1
52
-0.3
61**
-0.1
92**
-0.2
25**
(0
.10)
(0
.13)
(0
.17)
(0
.12)
(0
.15)
(0
.16)
(0
.084
) (0
.11)
Fo
reca
st e
rror
(inf
latio
n)
0.
0171
(0
.061
)
Fo
reca
st e
rror
(un
r)
0.
146
(0.1
7)
Leng
th o
f Con
tract
(mon
ths)
0.
001*
*
(0
.000
56)
La
gged
Infla
tion
-0
.016
(0
.048
)
Le
vel o
f une
mpl
oym
ent r
ate
(for
ecas
t)
0.
005
-0.2
07**
(0.0
78)
(0.1
0)
Leve
l of u
nem
ploy
men
t rat
e (c
urre
nt)
0.
317*
**
(0.0
89)
Con
stan
t, Ti
me
Dum
mie
s Y
ES
YES
Y
ES
YES
Y
ES
YES
Y
ES
YES
Y
ES
YES
O
bser
vatio
ns
2621
12
83
1338
20
90
1446
26
21
2621
26
21
2621
26
21
Num
ber o
f gro
ups
100
100
100
79
55
100
100
100
100
100
Sum
: no
rmin
flˆ
ˆ
1.03
3 0.
976
0.96
8 1.
045
1.04
1 1.
03
1.03
2 1.
056
1.01
9 1.
107
Prob
abili
ty v
alue
of H
0 1
ˆˆ
norm
infl
0.
172
0.46
9 0.
66
0.10
7 0.
277
0.33
4 0.
114
0.31
8 0.
707
0.04
5
Note
: The
col
umns
con
tain
var
ious
robu
stne
ss te
sts
to th
e be
nchm
ark
estim
atio
n w
ith le
ader
ship
refe
renc
e no
rms
in c
olum
n (7
) of T
able
4b,
her
e re
peat
ed in
col
umn
(1).
All
estim
atio
ns
incl
ude
(dec
ade)
tim
e du
mm
ies,
a co
nsta
nt te
rm a
nd th
ey a
re b
ased
on
RC
mod
els.
Stan
dard
err
ors
are
in p
aren
thes
es. *
**, *
* an
d *
deno
te s
tatis
tical
sig
nific
ance
at t
he 1
, 5 a
nd 1
0 %
le
vel,
resp
ectiv
ely.
61ECB
Working Paper Series No 1047April 2009
Figure 2 – The Reaction of the Individual Wage-Setting Units
Coefficients of the expected change in the unemployment rate i
2ˆ
Coefficients of the reference norm i3
ˆ Panel A: No Reference Norms
-3-2
.5-2
-1.5
-1-.5
0.5
Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct
Coefficients of the change in the unemployment rate(no reference norms)
Panel B: External Reference Norms
-3-2
.5-2
-1.5
-1-.5
0.5
Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct
Coefficients of the change in the unemployment rate(external norms)
0.2
5.5
.75
1
Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct
Coefficients of the reference norm(external norms)
Panel C: Leadership Reference Norms
-3-2
.5-2
-1.5
-1-.5
0.5
Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct
Coefficients of the change in the unemployment rate(leadership norms)
0.2
5.5
.75
1
Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct
Coefficients of the reference norm(leadership norms)
Note: The graphs report the coefficients for the expected change in the unemployment rate and the reference norm for the 100 individual wage-setting units when the benchmark equation is estimated with a random coefficients model. The individual coefficients are ordered according to the typical (median) month in which each wage-setting unit has concluded its wage agreements.
62ECBWorking Paper Series No 1047April 2009
European Central Bank Working Paper Series
For a complete list of Working Papers published by the ECB, please visit the ECB’s website
(http://www.ecb.europa.eu).
989 “Modelling loans to non-financial corporations in the euro area” by C. Kok Sørensen, D. Marqués-Ibáñez
and C. Rossi, January 2009
990 “Fiscal policy, housing and stock prices” by A. Afonso and R. M. Sousa, January 2009.
991 “The macroeconomic effects of fiscal policy” by A. Afonso and R. M. Sousa, January 2009.
992 “FDI and productivity convergence in central and eastern Europe: an industry-level investigation”
by M. Bijsterbosch and M. Kolasa, January 2009.
993 “Has emerging Asia decoupled? An analysis of production and trade linkages using the Asian international
input-output table” by G. Pula and T. A. Peltonen, January 2009.
994 “Fiscal sustainability and policy implications for the euro area” by F. Balassone, J. Cunha, G. Langenus, B. Manzke,
J. Pavot, D. Prammer and P. Tommasino, January 2009.
995 “Current account benchmarks for central and eastern Europe: a desperate search?” by M. Ca’ Zorzi, A. Chudik
and A. Dieppe, January 2009.
996 “What drives euro area break-even inflation rates?” by M. Ciccarelli and J. A. García, January 2009.
997 “Financing obstacles and growth: an analysis for euro area non-financial corporations” by C. Coluzzi, A. Ferrando
and C. Martinez-Carrascal, January 2009.
998 “Infinite-dimensional VARs and factor models” by A. Chudik and M. H. Pesaran, January 2009.
999 “Risk-adjusted forecasts of oil prices” by P. Pagano and M. Pisani, January 2009.
1000 “Wealth effects in emerging market economies” by T. A. Peltonen, R. M. Sousa and I. S. Vansteenkiste,
January 2009.
1001 “Identifying the elasticity of substitution with biased technical change” by M. A. León-Ledesma, P. McAdam
and A. Willman, January 2009.
1002 “Assessing portfolio credit risk changes in a sample of EU large and complex banking groups in reaction
to macroeconomic shocks” by O. Castrén, T. Fitzpatrick and M. Sydow, February 2009.
1003 “Real wages over the business cycle: OECD evidence from the time and frequency domains” by J. Messina,
C. Strozzi and J. Turunen, February 2009.
1004 “Characterising the inflation targeting regime in South Korea” by M. Sánchez, February 2009.
1005 “Labor market institutions and macroeconomic volatility in a panel of OECD countries” by F. Rumler
and J. Scharler, February 2009.
1006 “Understanding sectoral differences in downward real wage rigidity: workforce composition, institutions,
technology and competition” by P. Du Caju, C. Fuss and L. Wintr, February 2009.
1007 “Sequential bargaining in a new-Keynesian model with frictional unemployment and staggered wage negotiation”
by G. de Walque, O. Pierrard, H. Sneessens and R. Wouters, February 2009.
63ECB
Working Paper Series No 1047April 2009
1008 “Liquidity (risk) concepts: definitions and interactions” by K. Nikolaou, February 2009.
1009 “Optimal sticky prices under rational inattention” by B. Maćkowiak and M. Wiederholt, February 2009.
1010 “Business cycles in the euro area” by D. Giannone, M. Lenza and L. Reichlin, February 2009.
1011 “The global dimension of inflation – evidence from factor-augmented Phillips curves” by S. Eickmeier and K. Moll,
February 2009.
1012 “Petrodollars and imports of oil exporting countries” by R. Beck and A. Kamps, February 2009.
1013 “Structural breaks, cointegration and the Fisher effect” by A. Beyer, A. A. Haug and B. Dewald, February 2009.
1014 “Asset prices and current account fluctuations in G7 economies” by M. Fratzscher and R. Straub, February 2009.
1015 “Inflation forecasting in the new EU Member States” by O. Arratibel, C. Kamps and N. Leiner-Killinger,
February 2009.
1016 “When does lumpy factor adjustment matter for aggregate dynamics?” by S. Fahr and F. Yao, March 2009.
1017 “Optimal prediction pools” by J. Geweke and G. Amisano, March 2009.
1018 “Cross-border mergers and acquisitions: financial and institutional forces” by N. Coeurdacier, R. A. De Santis
and A. Aviat, March 2009.
1019 “What drives returns to euro area housing? Evidence from a dynamic dividend-discount model” by P. Hiebert
and M. Sydow, March 2009.
1020 “Opting out of the Great Inflation: German monetary policy after the break down of Bretton Woods”
by A. Beyer, V. Gaspar, C. Gerberding and O. Issing, March 2009.
1021 “Rigid labour compensation and flexible employment? Firm-level evidence with regard to productivity for
Belgium” by C. Fuss and L. Wintr, March 2009.
1022 “Understanding inter-industry wage structures in the euro area” by V. Genre, K. Kohn and D. Momferatou,
March 2009.
1023 “Bank loan announcements and borrower stock returns: does bank origin matter?” by S. Ongena
and V. Roscovan, March 2009.
1024 “Funding liquidity risk: definition and measurement” by M. Drehmann and K. Nikolaou, March 2009.
1025 “Liquidity risk premia in unsecured interbank money markets” by J. Eisenschmidt and J. Tapking, March 2009.
1026 “Do house price developments spill over across euro area countries? Evidence from a global VAR”
by I. Vansteenkiste and P. Hiebert, March 2009.
1027 “Long run evidence on money growth and inflation” by L. Benati, March 2009.
1028 “Large debt financing: syndicated loans versus corporate bonds” by Y. Altunbaș, A. Kara and D. Marqués-Ibáñez,
March 2009.
1029 “The role of fiscal transfers for regional economic convergence in Europe” by C. Checherita, C. Nickel
and P. Rother, March 2009.
1030 “Forecast evaluation of small nested model sets” by K. Hubrich and K. D. West, March 2009.
64ECBWorking Paper Series No 1047April 2009
1031 “Global roles of currencies” by C. Thimann, March 2009.
1032 “Assessing long-term fiscal developments: a new approach” by A. Afonso, L. Agnello, D. Furceri and R. Sousa,
March 2009.
1033 “Fiscal competition over taxes and public inputs: theory and evidence” by S. Hauptmeier, F. Mittermaier
and J. Rincke, March 2009.
1034 “The role of the United States in the global economy and its evolution over time” by S. Dées
and A. Saint-Guilhem, March 2009.
1035 “The role of labor markets for euro area monetary policy” by K. Christoffel, K. Kuester and T. Linzert,
March 2009.
1036 “Search in the product market and the real business cycle” by T. Y. Mathä and O. Pierrard, March 2009.
1037 “What do asset prices have to say about risk appetite and uncertainty?” by G. Bekaert, M. Hoerova
and M. Scheicher, March 2009.
1038 “Are ‘intrinsic inflation persistence’ models structural in the sense of Lucas (1976)?” by L. Benati, March 2009.
1039 “‘Real Time’ early warning indicators for costly asset price boom/bust cycles: a role for global liquidity”
by L. Alessi and C. Detken, March 2009.
1040 “The external and domestic side of macroeconomic adjustment in China” by R. Straub and C. Thimann,
March 2009.
1041 “An economic capital integrating credit and interest rate risk in the banking book” by P. Alessandri
and M. Drehmann, April 2009.
1042 “The determinants of public deficit volatility” by L. Agnello and R. M. Sousa, April 2009.
1043 “Optimal monetary policy in a model of the credit channel” by F. De Fiore and O. Tristani, April 2009.
1044 “The forecasting power of international yield curve linkages” by M. Modugno and K. Nikolaou, April 2009.
1045 “The term structure of equity premia in an affine arbitrage-free model of bond and stock market dynamics”
by W. Lemke and T. Werner, April 2009.
1046 “Productivity shocks and real exchange rates: a reappraisal” by T. A. Peltonen and M. Sager, April 2009.
1047 “The impact of reference norms on inflation persistence when wages are staggered” by M. Knell
and A. Stiglbauer, April 2009.